Showing papers in "International Journal for Numerical Methods in Fluids in 2016"

2D Burgers equation with large Reynolds number using POD/DEIM and calibration

Abstract: Summary Model order reduction of the two-dimensional Burgers equation is investigated. The mathematical formulation of POD/discrete empirical interpolation method (DEIM)-reduced order model (ROM) is derived based on the Galerkin projection and DEIM from the existing high fidelity-implicit finite-difference full model. For validation, we numerically compared the POD ROM, POD/DEIM, and the full model in two cases of Re = 100 and Re = 1000, respectively. We found that the POD/DEIM ROM leads to a speed-up of CPU time by a factor of O(10). The computational stability of POD/DEIM ROM is maintained by means of a careful selection of POD modes and the DEIM interpolation points. The solution of POD/DEIM in the case of Re = 1000 has an accuracy with error O(10−3) versus O(10−4) in the case of Re = 100 when compared with the high fidelity model. For this turbulent flow, a closure model consisting of a Tikhonov regularization is carried out in order to recover the missing information and is developed to account for the small-scale dissipation effect of the truncated POD modes. It is shown that the computational results of this calibrated ROM exhibit considerable agreement with the high fidelity model, which implies the efficiency of the closure model used. Copyright © 2016 John Wiley & Sons, Ltd.

Mesh adaptation for large‐eddy simulations in complex geometries

Abstract: Large-eddy simulation (LES) consists in explicitly simulating the large scales of the fluid motion and in modeling the influence of the smallest scales. Thanks to the steady growth of computational resources, LES can now be used to simulate realistic systems with complex geometries. However, when LES is used in such complex geometries, an adequate mesh has to be determined to perform valid LES. In this work, a strategy is proposed to assess the quality of a given mesh and to adapt it locally. Two different criteria are used as mesh adaptation criteria. The first criterion is defined to ensure a correct discretization of the mean field, whereas the second criterion is defined to ensure enough explicit resolution of turbulent scales motions. The use of both criteria is shown in canonical flow cases. As a second part of this work, a numerical strategy for mesh adaptation in high-performance computing context is proposed by coupling the flow solver, YALES2, and the remeshing library, MMG3D, for massively parallel computations. This coupling enables an efficient and parallel remeshing of grids alleviating any memory or performance issues encountered in sequential tools. This strategy is finally applied to the simulation of the isothermal flow in a complex meso-combustor to demonstrate the applicability of the adaptation methodology to complex turbulent flows.

L2Roe: A low-dissipation version of Roe's approximate Riemann solver for low Mach numbers

Abstract: A modification of the Roe scheme called L2Roe for low dissipation low Mach Roe is presented. It reduces the dissipation of kinetic energy at the highest resolved wave numbers in a low Mach number test case of decaying isotropic turbulence. This is achieved by scaling the jumps in all discrete velocity components within the numerical flux function. An asymptotic analysis is used to show the correct pressure scaling at low Mach numbers and to identify the reduced numerical dissipation in that regime. Furthermore, the analysis allows a comparison with two other schemes that employ different scaling of discrete velocity jumps, namely, LMRoe and a method of Thornber et al. To this end, we present for the first time an asymptotic analysis of the last method. Numerical tests on cases ranging from low Mach number (M∞=0.001) to hypersonic (M∞=5) viscous flows are used to illustrate the differences between the methods and to show the correct behavior of L2Roe. No conflict is observed between the reduced numerical dissipation and the accuracy or stability of the scheme in any of the investigated test cases. (Less)

Implicit large eddy simulation using the high-order correction procedure via reconstruction scheme

Abstract: Summary We investigate implicit large eddy simulation of the Taylor–Green vortex, Comte-Bellot–Corrsin experiment, turbulent channel flow and transitional and turbulent flow over an SD7003 airfoil using the high-order unstructured correction procedure via reconstruction (CPR) scheme, also known as the flux reconstruction scheme. We employ P1 (second-order) to P5 (sixth-order) spatial discretizations. Results show that the CPR scheme can accurately predict turbulent flows without the addition of a sub-grid scale model. Numerical dissipation, concentrated at the smallest resolved scales, is found to filter high-frequency content from the solution. In addition, the high-order schemes are found to be more accurate than the low-order schemes on a per degree of freedom basis for the canonical test cases we consider. These results motivate the further investigation and use of the CPR scheme for simulating turbulent flows. Copyright © 2016 John Wiley & Sons, Ltd.

Numerical Study of the Properties of the Central Moment Lattice Boltzmann Method

Abstract: Central moment lattice Boltzmann method (LBM) is one of the more recent developments among the lattice kinetic schemes for computational fluid dynamics. A key element in this approach is the use of central moments to specify collision process and forcing, and thereby naturally maintaining Galilean invariance, an important characteristic of fluid flows. When the different central moments are relaxed at different rates like in a standard multiple relaxation time (MRT) formulation based on raw moments, it is endowed with a number of desirable physical and numerical features. Since the collision operator exhibits a cascaded structure, this approach is also known as the cascaded LBM. While the cascaded LBM has been developed sometime ago, a systematic study of its numerical properties, such as accuracy, grid convergence and stability for well defined canonical problems is lacking and the present work is intended to fulfill this need. We perform a quantitative study of the performance of the cascaded LBM for a set of benchmark problems of differing complexity, viz., Poiseuille flow, decaying Taylor-Green vortex flow and lid-driven cavity flow. We first establish its grid convergence and demonstrate second order accuracy under diffusive scaling for both the velocity field and its derivatives, i.e. components of the strain rate tensor, as well. The method is shown to quantitatively reproduce steady/unsteady analytical solutions or other numerical results with excellent accuracy. Numerical experiments further demonstrate that the central moment MRT LBM results in significant stability improvements when compared with certain existing collision models at moderate additional computational cost.

POD–Galerkin monolithic reduced order models for parametrized fluid‐structure interaction problems

Abstract: Summary In this paper, we propose a monolithic approach for reduced-order modeling of parametrized fluid-structure interaction problems based on a proper orthogonal decomposition–Galerkin method. Parameters of the problem are related to constitutive properties of the fluid or structural problem, or to geometrical parameters related to the domain configuration at the initial time. We provide a detailed description of the parametrized formulation of the multiphysics problem in its components, together with some insights on how to obtain an offline–online efficient computational procedure through the approximation of parametrized nonlinear tensors. Then, we present the monolithic proper orthogonal decomposition–Galerkin method for the online computation of the global structural displacement, fluid velocity, and pressure of the coupled problem. Finally, we show some numerical results to highlight the capabilities of the proposed reduced-order method and its computational performances. Copyright © 2016 John Wiley & Sons, Ltd.

A well-balanced scheme to capture non-explicit steady states in the Euler equations with gravity

Abstract: Summary This paper describes a numerical discretization of the compressible Euler equations with a gravitational potential. A pertinent feature of the solutions to these inhomogeneous equations is the special case of stationary solutions with zero velocity, described by a nonlinear partial differential equation, whose solutions are called hydrostatic equilibria. We present a well-balanced method, meaning that besides discretizing the complete equations, the method is also able to maintain all hydrostatic equilibria. The method is a finite volume method, whose Riemann solver is approximated by a so-called relaxation Riemann solution that takes all hydrostatic equilibria into account. Relaxation ensures robustness, accuracy, and stability of our method, because it satisfies discrete entropy inequalities. We will present numerical examples, illustrating that our method works as promised. Copyright © 2015 John Wiley & Sons, Ltd.

On linear and nonlinear aspects of dynamic mode decomposition

Abstract: The approximation of reduced linear evolution operator (propagator) via Dynamic Mode Decomposition is addressed for both linear and nonlinear events. The 2D unsteady supersonic underexpanded jet, impinging the flat plate in nonlinear oscillating mode, is used as the first test problem for both modes. Large memory savings for the propagator approximation are demonstrated. Corresponding prospects for the estimation of receptivity and singular vectors are discussed. The shallow water equations are used as the second large scale test problem. Excellent results are obtained for the proposed optimized DMD method of the shallow water equations when compared with recent POD/DEIM based model results in the literature.

Unsteady shock-fitting for unstructured grids

Abstract: Summary An unstructured, shock-fitting algorithm, originally developed to simulate steady flows, has being further developed to make it capable of dealing with unsteady flows. The present paper discusses and analyses the additional features required to extend to unsteady flows, the steady algorithm. The properties of the unsteady version of this novel, unstructured shock-fitting technique, are tested by reference to the inviscid interaction between a vortex and a planar shock: a comparative assessment of shock-capturing and shock-fitting is made for the same test problem. Copyright © 2015 John Wiley & Sons, Ltd.

An improved KGF‐SPH with a novel discrete scheme of Laplacian operator for viscous incompressible fluid flows

Abstract: Summary The kernel gradient free (KGF) smoothed particle hydrodynamics (SPH) method is a modified finite particle method (FPM) which has higher order accuracy than the conventional SPH method. In KGF-SPH, no kernel gradient is required in the whole computation, and this leads to good flexibility in the selection of smoothing functions and it is also associated with a symmetric corrective matrix. When modeling viscous incompressible flows with SPH, FPM or KGF-SPH, it is usual to approximate the Laplacian term with nested approximation on velocity, and this may introduce numerical errors from the nested approximation, and also cause difficulties in dealing with boundary conditions. In this paper, an improved KGF-SPH method is presented for modeling viscous, incompressible fluid flows with a novel discrete scheme of Laplacian operator. The improved KGF-SPH method avoids nested approximation of first order derivatives, and keeps the good feature of ‘kernel gradient free’. The two-dimensional incompressible fluid flow of shear cavity, both in Euler frame and Lagrangian frame, are simulated by SPH, FPM, the original KGF-SPH and improved KGF-SPH. The numerical results show that the improved KGF-SPH with the novel discrete scheme of Laplacian operator are more accurate than SPH, and more stable than FPM and the original KGF-SPH. Copyright © 2015 John Wiley & Sons, Ltd.

Deconvolution-based nonlinear filtering for incompressible flows at moderately large Reynolds numbers

Abstract: Summary We consider a Leray model with a deconvolution-based indicator function for the simulation of incompressible fluid flow at moderately large Reynolds number (in the range of a few thousands) with under-resolved meshes. For the implementation of the model, we adopt a three-step algorithm called evolve–filter–relax that requires (i) the solution of a Navier–Stokes problem, (ii) the solution of a Stokes-like problem to filter the Navier–Stokes velocity field, and (iii) a final relaxation step. We take advantage of a reformulation of the evolve–filter–relax algorithm as an operator-splitting method to analyze the impact of the filter on the final solution versus a direct simulation of the Navier–Stokes equations. In addition, we provide some direction for tuning the parameters involved in the model based on physical and numerical arguments. Our approach is validated against experimental data for fluid flow in an idealized medical device (consisting of a conical convergent, a narrow throat, and a sudden expansion, as recommended by the U.S. Food and Drug Administration). Numerical results are in good quantitative agreement with the measured axial components of the velocity and pressures for two different flow rates corresponding to turbulent regimes, even for meshes with a mesh size more than 40 times larger than the smallest turbulent scale. After several numerical experiments, we perform a preliminary sensitivity analysis of the computed solution to the parameters involved in the model. Copyright © 2015 John Wiley & Sons, Ltd.

Modeling of static contact angles with curved boundaries using a multiphase lattice Boltzmann method with variable density and viscosity ratios

Abstract: Summary Numerical modeling of multiphase flow generally requires a special procedure at the solid wall in order to be consistent with Young's law for static contact angles. The standard approach in the lattice Boltzmann method, which consists of imposing fictive densities at the solid lattice sites, is shown to be deficient for this task. Indeed, fictive mass transfer along the boundary could happen and potentially spoil the numerical results. In particular, when the contact angle is less than 90 degrees, the deficiencies of the standard model are major. Various videos that demonstrate this behavior are provided (Supporting Information). A new approach is proposed and consists of directly imposing the contact angle at the boundaries in much the same way as Dirichlet boundary conditions are generally imposed. The proposed method is able to retrieve analytical solutions for static contact angles in the case of straight and curved boundaries even when variable density and viscosity ratios between the phases are considered. Although the proposed wetting boundary condition is shown to significantly improve the numerical results for one particular class of lattice Boltzmann model, it is believed that other lattice Boltzmann multiphase schemes could also benefit from the underlying ideas of the proposed method. The proposed algorithm is two-dimensional, and the D2Q9 lattice is used. Copyright © 2016 John Wiley & Sons, Ltd.

Dilation-based shock capturing for high-order methods

Abstract: Summary In this paper, we introduce a shock-capturing artificial viscosity technique for high-order unstructured mesh methods. This artificial viscosity model is based on a non-dimensional form of the divergence of the velocity. The technique is an extension and improvement of the dilation-based artificial viscosity methods introduced in Premasuthan et al., [15] and further extended in Nguyen and Peraire [27]. The approach presented has a number attractive properties including non-dimensional analytical form, sub-cell resolution, and robustness for complex shock flows on anisotropic meshes. We present extensive numerical results to demonstrate the performance of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.

A local mesh refinement approach for large‐eddy simulations of turbulent flows

Abstract: In this paper, a local mesh refinement (LMR) scheme on Cartesian grids for large-eddy simulations is presented. The approach improves the calculation of ghost cell pressures and velocities and combines LMR with high-order interpolation schemes at the LMR interface and throughout the rest of the computational domain to ensure smooth and accurate transition of variables between grids of different resolution. The approach is validated for turbulent channel flow and flow over a matrix of wall-mounted cubes for which reliable numerical and experimental data are available. Comparisons of predicted first-order and second-order turbulence statistics with the validation data demonstrated a convincing agreement. Importantly, it is shown that mean streamwise velocities and fluctuating turbulence quantities transition smoothly across coarse-to-fine and fine-to-coarse interfaces.

A variable-fidelity aerodynamic model using proper orthogonal decomposition

Abstract: This work was conducted with support from the Engineering and Physical Sciences Research Council (EPSRC) Centre of Excellence for Industrial Sustainability grant number EP/I033351/1 (a research collaboration of Cambridge, Cranfield, Imperial and Loughborough Universities). No new data were created in the course of this work. The authors are grateful to Greg Boulton, Technology Enhanced Learning Designer at Cranfield University, for his help in creating Figure 1. The authors also acknowledge the pioneering work of Emeritus Professor David Tranfield who laid the foundations for systematic review in Management and Organizational Studies which continues to inspire.

Compressive advection and multi-component methods for interface-capturing

Abstract: This paper develops methods for interface-capturing in multiphase flows. The main novelties of these methods are as follows: (a) multi-component modelling that embeds interface structures into the continuity equation; (b) a new family of triangle/tetrahedron finite elements, in particular, the P1DG-P2(linear discontinuous between elements velocity and quadratic continuous pressure); (c) an interface-capturing scheme based on compressive control volume advection methods and high-order finite element interpolation methods; (d) a time stepping method that allows use of relatively large time step sizes; and (e) application of anisotropic mesh adaptivity to focus the numerical resolution around the interfaces and other areas of important dynamics. This modelling approach is applied to a series of pure advection problems with interfaces as well as to the simulation of the standard computational fluid dynamics benchmark test cases of a collapsing water column under gravitational forces (in two and three dimensions) and sloshing water in a tank. Two more test cases are undertaken in order to demonstrate the many-material and compressibility modelling capabilities of the approach. Numerical simulations are performed on coarse unstructured meshes to demonstrate the potential of the methods described here to capture complex dynamics in multiphase flows.

Multi-material closure model for high-order finite element Lagrangian hydrodynamics

Abstract: We present a new closure model for single fluid, multi-material Lagrangian hydrodynamics and its application to high-order finite element discretizations of these equations [1]. The model is general with respect to the number of materials, dimension, space and time discretization. Knowledge about exact material interfaces is not required. Material indicator functions are evolved by a closure computation at each quadrature point of mixed cells, which can be viewed as a high-order variational generalization of the method of Tipton [2]. This computation is defined by the notion of partial non-instantaneous pressure equilibration, while the full pressure equilibration is achieved by both the closure model and the hydrodynamic motion. Exchange of internal energy between materials is derived through entropy considerations, that is, every material produces positive entropy, and the total entropy production is maximized in compression and minimized in expansion. Results are presented for standard one-dimensional two-material problems, followed by twoand three-dimensional multi-material high-velocity impact arbitrary Lagrangian-Eulerian (ALE) calculations. Copyright c © 0000 John Wiley & Sons, Ltd.

A new numerical model for simulations of wave transformation, breaking and long-shore currents in complex coastal regions

Abstract: Summary In this paper, we propose a model based on a new contravariant integral form of the fully nonlinear Boussinesq equations in order to simulate wave transformation phenomena, wave breaking, and nearshore currents in computational domains representing the complex morphology of real coastal regions. The aforementioned contravariant integral form, in which Christoffel symbols are absent, is characterized by the fact that the continuity equation does not include any dispersive term. A procedure developed in order to correct errors related to the difficulties of numerically satisfying the metric identities in the numerical integration of fully nonlinear Boussinesq equation on generalized boundary-conforming grids is presented. The Boussinesq equation system is numerically solved by a hybrid finite volume–finite difference scheme. The proposed high-order upwind weighted essentially non-oscillatory finite volume scheme involves an exact Riemann solver and is based on a genuinely two-dimensional reconstruction procedure, which uses a convex combination of biquadratic polynomials. The wave breaking is represented by discontinuities of the weak solution of the integral form of the nonlinear shallow water equations. The capacity of the proposed model to correctly represent wave propagation, wave breaking, and wave-induced currents is verified against test cases present in the literature. The results obtained are compared with experimental measures, analytical solutions, or alternative numerical solutions. Copyright © 2015 John Wiley & Sons, Ltd.

An efficient and energy stable scheme for a phase‐field model for the moving contact line problem

Abstract: In this paper, we propose for the first time a linearly coupled, energy stable scheme for the Navier–Stokes– Cahn–Hilliard system with generalized Navier boundary condition. We rigorously prove the unconditional energy stability for the proposed time discretization as well as for a fully discrete finite element scheme. Using numerical tests, we verify the accuracy, confirm the decreasing property of the discrete energy, and demonstrate the effectiveness of our method through numerical simulations in both 2-D and 3-D. Copyright © 2015 John Wiley & Sons, Ltd.

The non‐reflective interface: an innovative forcing technique for computational acoustic hybrid methods

Abstract: Summary The present article concerns a commonly used methodology for the numerical simulation of acoustic emission and propagation phenomena. We consider the so-called multi-stage hybrid acoustic approach, in which a given noise problem is simulated via a sequence of weakly coupled computations of noise generation and acoustic propagation stages, wherein the simulation of the propagation stage is based on advanced Computational AeroAcoustics (CAA) techniques. The paper introduces an original forcing technique, namely, the Non-Reflective Interface (NRI), to enable the transfer of an acoustic signal from an a priori noise generation stage into a CAA-based acoustic propagation phase. Unlike most existing forcing techniques, the NRI is non-reflective (or anechoic) in nature and, therefore, can properly handle the backscattering effects arising during the noise propagation stage. This attribute makes the NRI-based weak-coupling procedure and the associated CAA-based hybrid approach compatible with a larger variety of realistic noise problems (such as those involving installed configurations in wind tunnel experiments, for instance). The NRI technique is first validated via several test cases of increasing complexity and is then applied to two aerodynamic noise problems. Copyright © 2015 John Wiley & Sons, Ltd. Copyright © 2015 John Wiley & Sons, Ltd.

Energy dissipative characteristic schemes for the diffusive Oldroyd-B viscoelastic fluid

Abstract: In this paper we propose new energy dissipative characteristic numerical methods for the approximation of diffusive Oldroyd-B equations, that are based either on the finite element or finite difference discretization. We prove energy stability of both schemes and illustrate their behaviour on a series of numerical experiments. Using both the diffusive model and the logarithmic transformation of the elastic stress we are able to obtain methods that converge as mesh parameter is refined. Copyright c © 0000 John Wiley & Sons, Ltd.