This paper explores the approximation power of Moving Least-Squares (MLS) approximations in the context of higher-order finite volume schemes on unstructured grids. The scope of the application of MLS is threefold: (1) computation of high-order derivatives of the field variables for a Godunov-type approach to hyperbolic problems or terms of hyperbolic character, (2) direct reconstruction of the fluxes at cell edges, for elliptic problems or terms of elliptic character, and (3) multiresolution shock detection and selective limiting. A major advantage of the proposed methodology over the most popular existing higher-order methods is related to the viscous discretization. The use of MLS approximations allows the direct reconstruction of high-order viscous fluxes using quite compact stencils, and without introducing new degrees of freedom, which results in a significant reduction in storage and workload. A selective limiting procedure is proposed, based on the multiresolution properties of the MLS approximants, which allows to switch off the limiters in smooth regions of the flow. Accuracy tests show that the proposed method achieves the expected convergence rates. Representative simulations show that the methodology is applicable to problems of engineering interest.

Finite volume solvers and movingleast-squares approximations for thecompressible Navier-Stokes equations onunstructured grids

We report development of a high-order compact flux reconstruction method for solving unsteady incompressible flow on unstructured grids with implicit dual time stepping. The method falls under the class of methods now referred to as flux reconstruction/correction procedure via reconstruction. The governing equations employ Chorin's classic artificial compressibility formulation with dual time stepping to solve unsteady flow problems. An implicit non-linear lower-upper symmetric Gauss-Seidel scheme with backward Euler discretization is used to efficiently march the solution in pseudo time, while a second-order backward Euler discretization is used to march in physical time. We verify and validate implementation of the high-order method coupled with our implicit time stepping scheme using both steady and unsteady incompressible flow problems. The current implicit time stepping scheme is proven effective in satisfying the divergence-free constraint on the velocity field in the artificial compressibility formulation within the context of the high-order flux reconstruction method. This compact high-order method is very suitable for parallel computing and can easily be extended to moving and deforming grids.

http://absimage.aps.org/image/DFD15/MWS_DFD15-2015-003322.pdf

A high-order solver for unsteady incompressible Navier-Stokes equations using the flux reconstruction method on unstructured grids with implicit dual time stepping

AMGCL is a header-only C++ library for the solution of large sparse linear systems with algebraic multigrid. The method may be used as a black-box solver for computational problems in various fields, since it does not require any information about the underlying geometry. AMGCL provides an efficient, flexible, and extensible implementation of several iterative solvers and preconditioners on top of different backends allowing the acceleration of the solution with the help of OpenMP, OpenCL, or CUDA technologies. Most algorithms have both shared memory and distributed memory implementations. The library is published under a permissive MIT license.

AMGCL – A C++ library for efficient solution of large sparse linear systems

Experimental study of the interaction of dambreak with a vertical cylinder

In this paper, a multiphase moving particle semi-implicit (MPS) method is developed by introduction of various multiphase models into the original MPS method for single-phase flows, and is then applied to the numerical simulations of two-layer-liquid and three-layer-liquid sloshing in a 2-D rectangular tank under different external excitations. To validate the accuracy of the present multiphase MPS method, the qualitative and quantitative results, including wave profiles, interface elevations and impact pressures, are compared with experimental data and other numerical results, which show a good agreement. In particular, the evolutions of free surface and phase interfaces are compared and an obvious discrepancy is found, indicating that the phase interfaces may suffer from complex deformations while the free surface keeps relatively quiet. Moreover, the different modes of phase interface are observed under different excitation frequencies. Then, the violent sloshing of a three-layer-liquid system is simulated and the phenomenon of internal wave breaking is well captured, which mainly benefitted from the Lagrangian basis of MPS method and its advantage in multiphase flows with complex interfaces. Finally, the three-layer-liquid sloshing with a vertical baffle are simulated to investigate the suppressing effect of baffle on multi-layer-liquid sloshing.

Numerical simulations of multi-layer-liquid sloshing by multiphase MPS method

The three-dimensionality extent of the dam break flow over a vertical wall is investigated numerically and experimentally in this paper. The numerical method is based on Reynolds averaged Navier-Stokes (RANS) equation that describes the three-dimensional incompressible turbulent flow. The free surface is captured by using the unstructured multi-dimensional interface capturing (UMTHINC) scheme. The equations are discretized on 2-D and 3-D unstructured grids using finite volume method. The numerical simulations are compared with newly conducted experiment with emphasis on the effect of three-dimensionality on both free surface and impact pressure. The comparison between the numerical and experimental results shows good agreement. Furthermore, the results also show that 3-D motion of the flow originates at the moment of impact at the lower corners of the impact wall and propagates to the inner region as time advances. The origin of the three-dimensionality is found to be the turbulence development as well as the relative velocity between the side wall region and the inner region of the wave front at the moment of impact.

Numerical and experimental investigation of three-dimensionality in the dam-break flow against a vertical wall

The purpose of the present research is to study three-dimensional lattice Boltzmann method (LBM) simulation on free surface impact phenomena with the validation on a newly performed dam breaking experiment. Large eddy simulation (LES) is implemented in the LBM to enhance the computational efficiency and to relax the restriction of the computational stability. The LBM method involves a surface-tracking technique with free surface algorithm. In this study, the present numerical simulation is validated by comparing wave front propagation and water level elevation with the experimental measurements. A three dimensional numerical simulation on dam breaking with vertical cylinder obstacles are performed and qualitative comparison with the experimental measurement has been made. Good qualitative agreement between numerical simulations and the experiments has been obtained in terms of free surface development, splash pattern and splash distance. For the square cross section cylinder, the water impacts on the cylinder violently and the flow is directed to the sides of the tank. For the circular cross section cylinder, the water flows smoothly around the cylinder and impacts tank wall violently. The results show that the free surface lattice Boltzmann method is efficient for dealing with complex geometrical problems.

/pdf/lattice-boltzmann-method-for-free-surface-impacting-on-3b6upov3pa.pdf

Lattice boltzmann method for free surface impacting on vertical cylinder: A comparison with experimental data

A high order flux reconstruction interface capturing method with a phase field preconditioning procedure

An unstructured mesh Reynolds-averaged Navier-Stokes (RANS) solver has been developed for numerical simulation of violent sloshing flows inside a tank with complicated inner structures. The numerical solver employs the unstructured multi-dimensional tangent hyperbolic interface capturing method (UMTHINC) for free-surface capturing combined with various turbulence models. The sloshing motion is numerically modeled using the body-force method which introduces a source term into the momentum equation corresponding to the tank motion profile. Numerical simulations of the tank sloshing problems are performed for different test cases with various oscillation frequencies. The performance of the interface capturing method has been discussed and the effect of turbulence model choice on loading predictions is highlighted by studying several RANS models and analyzing its effect on fluid motion and impact pressure. Numerical simulations of the sloshing inside the tank with a vertical baffle has also been conducted and a discussion is provided on different numerical treatment of the baffle.

Mohamed M. Kamra

Papers

Experimental study of the interaction of dambreak with a vertical cylinder

Numerical and experimental investigation of three-dimensionality in the dam-break flow against a vertical wall

Lattice boltzmann method for free surface impacting on vertical cylinder: A comparison with experimental data

A high order flux reconstruction interface capturing method with a phase field preconditioning procedure

An unstructured mesh method for numerical simulation of violent sloshing flows