Showing papers in "International Journal for Numerical Methods in Fluids in 2014"

High‐order discontinuous Galerkin spectral element methods for transitional and turbulent flow simulations

Abstract: SUMMARY In this paper, we investigate the accuracy and efficiency of discontinuous Galerkin spectral method simulations of under-resolved transitional and turbulent flows at moderate Reynolds numbers, where the accurate prediction of closely coupled laminar regions, transition and developed turbulence presents a great challenge to large eddy simulation modelling. We take full advantage of the low numerical errors and associated superior scale resolving capabilities of high-order spectral methods by using high-order ansatz functions up to 12th order. We employ polynomial de-aliasing techniques to prevent instabilities arising from inexact quadrature of nonlinearities. Without the need for any additional filtering, explicit or implicit modelling, or artificial dissipation, our high-order schemes capture the turbulent flow at the considered Reynolds number range very well. Three classical large eddy simulation benchmark problems are considered: a circular cylinder flow at ReD=3900, a confined periodic hill flow at Reh=2800 and the transitional flow over a SD7003 airfoil at Rec=60,000. For all computations, the total number of degrees of freedom used for the discontinuous Galerkin spectral method simulations is chosen to be equal or considerably less than the reported data in literature. In all three cases, we achieve an equal or better match to direct numerical simulation results, compared with other schemes of lower order with explicitly or implicitly added subgrid scale models. Copyright © 2014 John Wiley & Sons, Ltd.

Topology optimisation for natural convection problems

Abstract: This paper demonstrates the application of the density-based topology optimisation approach for the design of heat sinks and micropumps based on natural convection effects. The problems are modelled under the assumptions of steady-state laminar flow using the incompressible Navier-Stokes equations coupled to the convection-diffusion equation through the Boussinesq approximation. In order to facilitate topology optimisation, the Brinkman approach is taken to penalise velocities inside the solid domain and the effective thermal conductivity is interpolated in order to accommodate differences in thermal conductivity of the solid and fluid phases. The governing equations are discretised using stabilised finite elements and topology optimisation is performed for two different problems using discrete adjoint sensitivity analysis. The study shows that topology optimisation is a viable approach for designing heat sink geometries cooled by natural convection and micropumps powered by natural convection. Copyright c © 2013 John Wiley & Sons, Ltd.

Assessment of a discontinuous Galerkin method for the simulation of vortical flows at high Reynolds number

Abstract: SUMMARY This paper focuses on the assessment of a discontinuous Galerkin method for the simulation of vortical flows at high Reynolds number. The Taylor–Green vortex at Re = 1600 is considered. The results are compared with those obtained using a pseudo-spectral solver, converged on a 5123 grid and taken as the reference. The temporal evolution of the dissipation rate, visualisations of the vortical structures and the kinetic energy spectrum at the instant of maximal dissipation are compared to assess the results. At an effective resolution of 2883, the fourth-order accurate discontinuous Galerkin method (DGM) solution (p = 3) is already very close to the pseudo-spectral reference; the error on the dissipation rate is then essentially less than a percent, and the vorticity contours at times around the dissipation peak overlap everywhere. At a resolution of 3843, the solutions are indistinguishable. Then, an order convergence study is performed on the slightly under-resolved grid (resolution of 1923). From the fourth order, the decrease of the error is no longer significant when going to a higher order. The fourth-order DGM is also compared with an energy conserving fourth-order finite difference method (FD4). The results show that, for the same number of DOF and the same order of accuracy, the errors of the DGM computation are significantly smaller. In particular, it takes 7683 DOF to converge the FD4 solution. Finally, the method is also successfully applied on unstructured high quality meshes. It is found that the dissipation rate captured is not significantly impacted by the element type. However, the element type impacts the energy spectrum in the large wavenumber range and thus the small vortical structures. In particular, at the same resolution, the results obtained using a tetrahedral mesh are much noisier than those obtained using a hexahedral mesh. Those obtained using a prismatic mesh are already much better, yet still slightly noisier. Copyright © 2013 John Wiley & Sons, Ltd.

A simple sliding‐mesh interface procedure and its application to the CFD simulation of a tidal‐stream turbine

Abstract: An effective way of using CFD to simulate flow about a rotating device ? for example, a wind or marine turbine ? is to embed a rotating region of cells inside a larger, stationary domain, with a sliding interface between. This paper describes a simple but effective method for implementing this as an internal Dirichlet boundary condition, with interfacial values obtained by interpolation from halo nodes. The method is tested in two finite-volume codes: one using block-structured, and the other unstructured, meshes. Testing and verification is performed for flow around simple, isolated, rotating shapes (cylinder, sphere, cube), comparing, where possible, with experiment and the alternative CFD approach of fixed grid with moving walls. For all cases, flow variables are shown to vary smoothly across the sliding interface. Simulations of a tidal-stream turbine, including both rotor and support structure, are then performed and compared with towing-tank experiments from the University of Southampton. A comparison between CFD and experiment is made for thrust and power coefficients as a function of tip-speed ratio (TSR) using Reynolds averaged Navier-Stokes turbulence models and large-eddy simulation (LES). Performance of most models is good near the optimal TSR, but simulations underestimate mean thrust and power coefficients in off-design conditions, with the standard k-epsilon turbulence model performing noticeably worse than SST k-omega and Reynolds-stress-transport closures. LES gave good predictions of mean load coefficients and vital information about wake structures, but at substantial computational cost. Grid-sensitivity studies suggest that SST k- and Reynoldsstress-transport models give acceptable predictions of mean power and thrust coefficients on a single device using a mesh of about 4 million cells.

Comparison of POD reduced order strategies for the nonlinear 2D shallow water equations

Abstract: SUMMARY This paper introduces tensorial calculus techniques in the framework of POD to reduce the computational complexity of the reduced nonlinear terms. The resulting method, named tensorial POD, can be applied to polynomial nonlinearities of any degree p. Such nonlinear terms have an online complexity of O(kp+1), where k is the dimension of POD basis and therefore is independent of full space dimension. However, it is efficient only for quadratic nonlinear terms because for higher nonlinearities, POD model proves to be less time consuming once the POD basis dimension k is increased. Numerical experiments are carried out with a two-dimensional SWE test problem to compare the performance of tensorial POD, POD, and POD/discrete empirical interpolation method (DEIM). Numerical results show that tensorial POD decreases by 76× the computational cost of the online stage of POD model for configurations using more than 300,000 model variables. The tensorial POD SWE model was only 2 to 8× slower than the POD/DEIM SWE model but the implementation effort is considerably increased. Tensorial calculus was again employed to construct a new algorithm allowing POD/DEIM SWE model to compute its offline stage faster than POD and tensorial POD approaches. Copyright © 2014 John Wiley & Sons, Ltd.

Towards consistent hybrid overset mesh methods for rotorcraft CFD

Abstract: The overset mesh method chimera is popular within the rotorcraft research community, because the use of multiple, non-matching grids make the CFD simulations of bodies in relative motion much simpler. Consequently, the relative motion between the helicopter blades and fuselage can be accurately accounted for. In this paper, the method for treating overset grids within CFD codes is presented. It is compatible with multi-block, structured-grid solvers. The proposed method is based on hierarchy of overset, non-matching grids, whose cells are automatically identified as computational or non-computational and localised with respect to all grids they overlap with. The efficiency of the method relies on the hierarchical, multi-step approach, for the overset mesh localisation and the use of a tree search. Because of the high efficiency of the algorithm, the search for overlapping cells can be carried out on-the-fly, during time-marching of the unsteady, implicit CFD solver. In addition, the algorithm is suitable for parallel execution. The method has been demonstrated for several flows, ranging from simple aerofoils to rotor-body interaction. The paper presents and demonstrates the method and shows that it has a low CPU overhead. It also highlights the limitations of the method and suggests remedies for improvement.

CAD‐based shape optimisation with CFD using a discrete adjoint

Abstract: SUMMARY One of the major challenges of shape optimisation in practical industrial cases is to generically parametrise the wide range of complex shapes. A novel approach is presented, which takes CAD descriptions as input and produces the optimal shape in CAD form using the control points of the Non-Uniform Rational B-Splines (NURBS) boundary representation as design variables. An implementation of the NURBS equations in source allows to include the CAD-based shape deformation inside the design loop and evaluate its sensitivities efficiently and robustly. In order to maintain or establish the required level of geometric continuity across patch interfaces, geometric constraints are imposed on the control point displacements. The paper discusses the discrete adjoint flow solver used and the computation of the complete sensitivities of the design loop by differentiating all components using automatic differentiation tools. The resulting rich but smooth deformation space is demonstrated on the optimisation of a vehicle climate duct. Copyright © 2013 John Wiley & Sons, Ltd.

Connections between the discontinuous Galerkin method and high‐order flux reconstruction schemes

Abstract: SUMMARY With high-order methods becoming more widely adopted throughout the field of computational fluid dynamics, the development of new computationally efficient algorithms has increased tremendously in recent years. One of the most recent methods to be developed is the flux reconstruction approach, which allows various well-known high-order schemes to be cast within a single unifying framework. Whilst a connection between flux reconstruction and the more widely adopted discontinuous Galerkin method has been established elsewhere, it still remains to fully investigate the explicit connections between the many popular variants of the discontinuous Galerkin method and the flux reconstruction approach. In this work, we closely examine the connections between three nodal versions of tensor-product discontinuous Galerkin spectral element approximations and two types of flux reconstruction schemes for solving systems of conservation laws on quadrilateral meshes. The different types of discontinuous Galerkin approximations arise from the choice of the solution nodes of the Lagrange basis representing the solution and from the quadrature approximation used to integrate the mass matrix and the other terms of the discretization. By considering both linear and nonlinear advection equations on a regular grid, we examine the mathematical properties that connect these discretizations. These arguments are further confirmed by the results of an empirical numerical study. Copyright © 2014 John Wiley & Sons, Ltd.

A kinetic energy preserving nodal discontinuous Galerkin spectral element method

Abstract: SUMMARY In this work, we discuss the construction of a skew-symmetric discontinuous Galerkin (DG) collocation spectral element approximation for the compressible Euler equations. Starting from the skew-symmetric formulation of Morinishi, we mimic the continuous derivations on a discrete level to find a formulation for the conserved variables. In contrast to finite difference methods, DG formulations naturally have inter-domain surface flux contributions due to the discontinuous nature of the approximation space. Thus, throughout the derivations we accurately track the influence of the surface fluxes to arrive at a consistent formulation also for the surface terms. The resulting novel skew-symmetric method differs from the standard DG scheme by additional volume terms. Those volume terms have a special structure and basically represent the discretization error of the different product rules. We use the summation-by-parts (SBP) property of the Gauss–Lobatto-based DG operator and show that the novel formulation is exactly conservative for the mass, momentum, and energy. Finally, an analysis of the kinetic energy balance of the standard DG discretization shows that because of aliasing errors, a nonzero transport source term in the evolution of the discrete kinetic energy mean value may lead to an inconsistent increase or decrease in contrast to the skew-symmetric formulation. Furthermore, we derive a suitable interface flux that guarantees kinetic energy preservation in combination with the skew-symmetric DG formulation. As all derivations require only the SBP property of the Gauss–Lobatto-based DG collocation spectral element method operator and that the mass matrix is diagonal, all results for the surface terms can be directly applied in the context of multi-domain diagonal norm SBP finite difference methods. Numerical experiments are conducted to demonstrate the theoretical findings. Copyright © 2014 John Wiley & Sons, Ltd.

High‐order ADER‐WENO ALE schemes on unstructured triangular meshes—application of several node solvers to hydrodynamics and magnetohydrodynamics

Abstract: SUMMARY In this paper, we present a class of high-order accurate cell-centered arbitrary Lagrangian–Eulerian (ALE) one-step ADER weighted essentially non-oscillatory (WENO) finite volume schemes for the solution of nonlinear hyperbolic conservation laws on two-dimensional unstructured triangular meshes. High order of accuracy in space is achieved by a WENO reconstruction algorithm, while a local space–time Galerkin predictor allows the schemes to be high order accurate also in time by using an element-local weak formulation of the governing PDE on moving meshes. The mesh motion can be computed by choosing among three different node solvers, which are for the first time compared with each other in this article: the node velocity may be obtained either (i) as an arithmetic average among the states surrounding the node, as suggested by Cheng and Shu, or (ii) as a solution of multiple one-dimensional half-Riemann problems around a vertex, as suggested by Maire, or (iii) by solving approximately a multidimensional Riemann problem around each vertex of the mesh using the genuinely multidimensional Harten–Lax–van Leer Riemann solver recently proposed by Balsara et al. Once the vertex velocity and thus the new node location have been determined by the node solver, the local mesh motion is then constructed by straight edges connecting the vertex positions at the old time level tn with the new ones at the next time level tn + 1. If necessary, a rezoning step can be introduced here to overcome mesh tangling or highly deformed elements. The final ALE finite volume scheme is based directly on a space–time conservation formulation of the governing PDE system, which therefore makes an additional remapping stage unnecessary, as the ALE fluxes already properly take into account the rezoned geometry. In this sense, our scheme falls into the category of direct ALE methods. Furthermore, the geometric conservation law is satisfied by the scheme by construction. We apply the high-order algorithm presented in this paper to the Euler equations of compressible gas dynamics as well as to the ideal classical and relativistic magnetohydrodynamic equations. We show numerical convergence results up to fifth order of accuracy in space and time together with some classical numerical test problems for each hyperbolic system under consideration. Copyright © 2014 John Wiley & Sons, Ltd.

Lagrangian formulation for finite element analysis of quasi‐incompressible fluids with reduced mass losses

Abstract: SUMMARY We present a Lagrangian formulation for finite element analysis of quasi-incompressible fluids that has excellent mass preservation features. The success of the formulation lays on a new residual-based stabilized expression of the mass balance equation obtained using the finite calculus method. The governing equations are discretized with the FEM using simplicial elements with equal linear interpolation for the velocities and the pressure. The merits of the formulation in terms of reduced mass loss and overall accuracy are verified in the solution of 2D and 3D quasi-incompressible free-surface flow problems using the particle FEM (www.cimne.com/pfem). Examples include the sloshing of water in a tank, the collapse of one and two water columns in rectangular and prismatic tanks, and the falling of a water sphere into a cylindrical tank containing water. Copyright © 2014 John Wiley & Sons, Ltd.

A semi‐implicit numerical method for the free‐surface Navier–Stokes equations

Abstract: SUMMARY Semi-implicit methods are known for being the basis of simple, efficient, accurate, and stable numerical algorithms for simulating a large variety of geophysical free-surface flows. Geophysical flows are typically characterized by having a small vertical scale as compared with their horizontal extents. Hence, the hydrostatic approximation often applies, and the free surface can be conveniently represented by a single-valued function of the horizontal coordinates. In the present investigation, semi-implicit methods are extended to complex free-surface flows that are governed by the full incompressible Navier–Stokes equations and are delimited by solid boundaries and arbitrarily shaped free-surfaces. The primary dependent variables are the velocity components and the pressure. Finite difference equations for momentum, and a finite volume discretization for continuity, are derived in such a fashion that, after simple manipulation, the resulting pressure equation yields a well-posed piecewise linear system from which both the pressure and the fluid volume within each computational cell are naturally derived. This system is efficiently solved by a nested Newton type iterative scheme, and the resulting fluid volumes are assured to be nonnegative and bounded from above by the available cell volumes. The time step size is not restricted by stability conditions dictated by surface wave speed, but can be freely chosen just to achieve the desired accuracy. Several examples illustrate the model applicability to a large range of complex free-surface flows and demonstrate the effectiveness of the proposed algorithm. Copyright © 2013 John Wiley & Sons, Ltd.

Fast Ewald summation for Stokesian particle suspensions

Abstract: We present a numerical method for suspensions of spheroids of arbitrary aspect ratio, which sediment under gravity. The method is based on a periodized boundary integral formulation using the Stoke ...

An efficient and accurate algebraic interface capturing method for unstructured grids in 2 and 3 dimensions: The THINC method with quadratic surface representation

Abstract: SUMMARY We present in this paper an efficient and accurate volume of fluid (VOF) type scheme to compute moving interfaces on unstructured grids with arbitrary quadrilateral mesh elements in 2D and hexahedral elements in 3D. Being an extension of the multi-dimensional tangent of hyperbola interface capturing (THINC) reconstruction proposed by the authors in Cartesian grid, an algebraic VOF scheme is devised for arbitrary quadrilateral and hexahedral elements. The interface is cell-wisely approximated by a quadratic surface, which substantially improves the numerical accuracy. The same as the other THINC type schemes, the present method does not require the explicit geometric representation of the interface when computing numerical fluxes and thus is very computationally efficient and straightforward in implementation. The proposed scheme has been verified by benchmark tests, which reveal that this scheme is able to produce high-quality numerical solutions of moving interfaces in unstructured grids and thus a practical method for interfacial multi-phase flow simulations. Copyright © 2014 John Wiley & Sons, Ltd.

Low cost 3D global instability analysis and flow sensitivity based on dynamic mode decomposition and high‐order numerical tools

Abstract: We explore the recently developed snapshot-based dynamic mode decomposition (DMD) technique, a matrix-free Arnoldi type method, to predict 3D linear global flow instabilities. We apply the DMD technique to flows confined in an L-shaped cavity and compare the resulting modes to their counterparts issued from classic, matrix forming, linear instability analysis (i.e. BiGlobal approach) and direct numerical simulations. Results show that the DMD technique, which uses snapshots generated by a 3D non-linear incompressible discontinuous Galerkin Navier?Stokes solver, provides very similar results to classical linear instability analysis techniques. In addition, we compare DMD results issued from non-linear and linearised Navier?Stokes solvers, showing that linearisation is not necessary (i.e. base flow not required) to obtain linear modes, as long as the analysis is restricted to the exponential growth regime, that is, flow regime governed by the linearised Navier?Stokes equations, and showing the potential of this type of analysis based on snapshots to general purpose CFD codes, without need of modifications. Finally, this work shows that the DMD technique can provide three-dimensional direct and adjoint modes through snapshots provided by the linearised and adjoint linearised Navier?Stokes equations advanced in time. Subsequently, these modes are used to provide structural sensitivity maps and sensitivity to base flow modification information for 3D flows and complex geometries, at an affordable computational cost. The information provided by the sensitivity study is used to modify the L-shaped geometry and control the most unstable 3D mode.

Analysis of multifluid flows with large time steps using the particle finite element method

Abstract: SUMMARY Multifluids are those fluids in which their physical properties (viscosity or density) vary internally and abruptly forming internal interfaces that introduce a large nonlinearity in the Navier–Stokes equations. For this reason, standard numerical methods require very small time steps in order to solve accurately the internal interface position. In a previous paper, the authors developed a particle-based method (named particle finite element method (PFEM)) based on a Lagrangian formulation and FEM for solving the fluid mechanics equations for multifluids. PFEM was capable of achieving accurate results, but the limitation of small time steps was still present. In this work, a new strategy concerning the time integration for the analysis of multifluids is developed allowing time steps one order of magnitude larger than the previous method. The advantage of using a Lagrangian solution with PFEM is shown in several examples. All kind of heterogeneous fluids (with different densities or viscosities), multiphase flows with internal interfaces, breaking waves, and fluid separation may be easily solved with this methodology without the need of small time steps. Copyright © 2014 John Wiley & Sons, Ltd.

A fixed‐grid b‐spline finite element technique for fluid–structure interaction

Abstract: We present a fixed-grid finite element technique for fluid-structure interaction problems involving incompressible viscous flows and thin structures. The flow equations are discretised with isoparametric b-spline basis functions defined on a logically Cartesian grid. In addition, the previously proposed subdivision-stabilisation technique is used to ensure inf-sup stability. The beam equations are discretised with b-splines and the shell equations with subdivision basis functions, both leading to a rotation-free formulation. The interface conditions between the fluid and the structure are enforced with the Nitsche technique. The resulting coupled system of equations is solved with a Dirichlet-Robin partitioning scheme, and the fluid equations are solved with a pressure-correction method. Auxiliary techniques employed for improving numerical robustness include the level-set based implicit representation of the structure interface on the fluid grid, a cut-cell integration algorithm based on marching tetrahedra and the conservative data transfer between the fluid and structure discretisations. A number of verification and validation examples, primarily motivated by animal locomotion in air or water, demonstrate the robustness and efficiency of our approach. © 2013 John Wiley & Sons, Ltd.

A detailed study of lid-driven cavity flow at moderate Reynolds numbers using Incompressible SPH

Abstract: Lid-driven cavity flow at moderate Reynolds numbers is studied here, employing a mesh-free method known as Smoothed Particle Hydrodynamics (SPH). In a detailed study of this benchmark, the incompressible SPH approach is applied together with a particle shifting algorithm. Additionally, a new treatment for no-slip boundary conditions is developed and tested. The use of the aforementioned numerical treatment for solid walls leads to significant improvements in the results with respect to other SPH simulations carried out with similar spatial resolution. However, the effect of spatial resolution is not considered in the present study as the number of particles used in each case was kept constant, approximately reproducing the same resolutions employed in reference studies available in the literature as well. Altogether, the detailed comparisons of field variables at discreet points demonstrate the accuracy and robustness of the new SPH method. Copyright © 2014 John Wiley & Sons, Ltd.

Direct and adjoint global stability analysis of turbulent transonic flows over a NACA0012 profile

Abstract: SUMMARY In this work, various turbulent solutions of the two-dimensional (2D) and three-dimensional compressible Reynolds averaged Navier–Stokes equations are analyzed using global stability theory. This analysis is motivated by the onset of flow unsteadiness (Hopf bifurcation) for transonic buffet conditions where moderately high Reynolds numbers and compressible effects must be considered. The buffet phenomenon involves a complex interaction between the separated flow and a shock wave. The efficient numerical methodology presented in this paper predicts the critical parameters, namely, the angle of attack and Mach and Reynolds numbers beyond which the onset of flow unsteadiness appears. The geometry, a NACA0012 profile, and flow parameters selected reproduce situations of practical interest for aeronautical applications. The numerical computation is performed in three steps. First, a steady baseflow solution is obtained; second, the Jacobian matrix for the RANS equations based on a finite volume discretization is computed; and finally, the generalized eigenvalue problem is derived when the baseflow is linearly perturbed. The methodology is validated predicting the 2D Hopf bifurcation for a circular cylinder under laminar flow condition. This benchmark shows good agreement with the previous published computations and experimental data. In the transonic buffet case, the baseflow is computed using the Spalart–Allmaras turbulence model and represents a mean flow where the high frequency content and length scales of the order of the shear-layer thickness have been averaged. The lower frequency content is assumed to be decoupled from the high frequencies, thus allowing a stability analysis to be performed on the low frequency range. In addition, results of the corresponding adjoint problem and the sensitivity map are provided for the first time for the buffet problem. Finally, an extruded three-dimensional geometry of the NACA0012 airfoil, where all velocity components are considered, was also analyzed as a Triglobal stability case, and the outcoming results were compared to the previous 2D limited model, confirming that the buffet onset is well detected. Copyright © 2014 John Wiley & Sons, Ltd.

Numerical simulation of transpiration cooling through porous material

Abstract: Transpiration cooling using ceramic matrix composite (CMC) materials is an innovative concept for cooling rocket thrust chambers. The coolant (air) is driven through the porous material by a pressure difference between the coolant reservoir and the turbulent hot gas flow. The effectiveness of such cooling strategies relies on a proper choice of the involved process parameters such as injection pressure, blowing ratios, material structure parameters, to name only a few. In view of the limited experimental access to the subtle processes occurring at the interface between hot gas flow and porous medium, reliable and accurate simulations become an increasingly important design tool. In order to facilitate such numerical simulations for a carbon/carbon material mounted in the side wall of a hot gas channel that are able to capture a spatially varying interplay between the hot gas flow and the coolant at the interface, we formulate a two dimensional model for the porous medium flow of Darcy-Forchheimer type. A finite element solver for the corresponding porous media flow is presented and coupled with a finite volume solver for the compressible Reynolds averaged Navier-Stokes equations. The results at Mach numberMa = 0.5 and hot gas temperature Thg = 540K for different blowing ratios are compared with experiments.

An SPH model for free surface flows with moving rigid objects

Abstract: This paper presents a computational model for free surface flows interacting with moving rigid bodies. The model is based on the SPH method, which is a popular meshfree, Lagrangian particle method and can naturally treat large flow deformation and moving features without any interface/surface capture or tracking algorithm. Fluid particles are used to model the free surface flows which are governed by Navier-Stokes equations, and solid particles are used to model the dynamic movement (translation and rotation) of moving rigid objects. The interaction of the neighboring fluid and solid particles renders the fluid-solid interaction and the non-slip solid boundary conditions. The SPH method is improved with corrections on the SPH kernel and kernel gradients, enhancement of solid boundary condition, and implementation of Reynolds-averaged Navier-Stokes turbulence model. Three numerical examples including the water exit of a cylinder, the sinking of a submerged cylinder and the complicated motion of an elliptical cylinder near free surface are provided. The obtained numerical results show good agreement with results from other sources and clearly demonstrate the effectiveness of the presented meshfree particle model in modeling free surface flows with moving objects

A Modular, Operator Splitting Scheme for Fluid-Structure Interaction Problems with Thick Structures

Abstract: We present an operator-splitting scheme for fluid-structure interaction (FSI) problems in hemodynamics, where the thickness of the structural wall is comparable to the radius of the cylindrical fluid domain. The equations of linear elasticity are used to model the structure, while the Navier-Stokes equations for an incompressible viscous fluid are used to model the fluid. The operator splitting scheme, based on Lie splitting, separates the elastodynamics structure problem, from a fluid problem in which structure inertia is included to achieve unconditional stability. We prove energy estimates associated with unconditional stability of this modular scheme for the full nonlinear FSI problem defined on a moving domain, without requiring any sub-iterations within time steps. Two numerical examples are presented, showing excellent agreement with the results of monolithic schemes. First-order convergence in time is shown numerically. Modularity, unconditional stability without temporal sub-iterations, and simple implementation are the features that make this operator-splitting scheme particularly appealing for multi-physics problems involving fluid-structure interaction.

An extended mixture model for the simultaneous treatment of small‐scale and large‐scale interfaces

Abstract: Fil: Marquez Damian, Santiago. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Centro Cientifico Tecnologico Conicet - Santa Fe. Centro de Investigaciones En Metodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones En Metodos Computacionales; Argentina

Adjoint-based error estimation and mesh adaptation for hybridized discontinuous Galerkin methods

Abstract: Summary We present a robust and efficient target-based mesh adaptation methodology, building on hybridized discontinuous Galerkin schemes for (nonlinear) convection–diffusion problems, including the compressible Euler and Navier–Stokes equations. The hybridization of finite element discretizations has the main advantage that the resulting set of algebraic equations has globally coupled degrees of freedom (DOFs) only on the skeleton of the computational mesh. Consequently, solving for these DOFs involves the solution of a potentially much smaller system. This not only reduces storage requirements but also allows for a faster solution with iterative solvers. The mesh adaptation is driven by an error estimate obtained via a discrete adjoint approach. Furthermore, the computed target functional can be corrected with this error estimate to obtain an even more accurate value. The aim of this paper is twofold: Firstly, to show the superiority of adjoint-based mesh adaptation over uniform and residual-based mesh refinement and secondly, to investigate the efficiency of the global error estimate. Copyright © 2014 John Wiley & Sons, Ltd.

Discontinuous Galerkin methods on graphics processing units for nonlinear hyperbolic conservation laws

Abstract: We present a novel implementation of the modal discontinuous Galerkin (DG) method for hyperbolic conservation laws in two dimensions on graphics processing units (GPUs) using NVIDIA's Compute Unified Device Architecture (CUDA). Both flexible and highly accurate, DG methods accommodate parallel architectures well as their discontinuous nature produces element-local approximations. High performance scientific computing suits GPUs well, as these powerful, massively parallel, cost-effective devices have recently included support for double-precision floating point numbers. Computed examples for Euler equations over unstructured triangle meshes demonstrate the effectiveness of our implementation on an NVIDIA GTX 580 device. Profiling of our method reveals performance comparable to an existing nodal DG-GPU implementation for linear problems.

A compatibly differenced total energy conserving form of SPH

Abstract: SUMMARY We describe a modified form of smoothed particle hydrodynamics (SPH) in which the specific thermal energy equation is based on a compatibly differenced formalism, guaranteeing exact conservation of the total energy. We compare the errors and convergence rates of the standard and compatible SPH formalisms on a variety of shock test problems with analytic answers. We find that the new compatible formalism reliably achieves the expected first-order convergence for these analytic shock tests and, in all cases, improves the accuracy of the numerical solution over the standard formalism. We also examine the performance of our new formalism on a more complicated applied problem: the diversion of an asteroid by a kinetic impactor. We find the compatible discretization demonstrates measurable improvement in the convergence of properties such as the deflection velocity in this kind of applied problem as well. Copyright © 2014 John Wiley & Sons, Ltd.