[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.12989/csm.2020.9.1.063

Towards isotropic transport with co-meshes

Paulin, Christina (CEA, DAM, DIF)
de Montigny, Eric Heulhard (CEA, DAM, DIF)
Llor, Antoine (CEA, DAM, DIF)

Publication Information

Coupled systems mechanics / v.9, no.1, 2020 , pp. 63-75 More about this Journal

Abstract

Transport is the central ingredient of all numerical schemes for hyperbolic partial differential equations and in particular for hydrodynamics. Transport has thus been extensively studied in many of its features and for numerous specific applications. In more than one dimension, it is most commonly plagued by a major artifact: mesh imprinting. Though mesh imprinting is generally inevitable, its anisotropy can be modulated and is thus amenable to significant reduction. In the present work we introduce a new definition of stencils by taking into account second nearest neighbors (across cell corners) and call the resulting strategy "co-mesh approach". The modified equation is used to study numerical dissipation and tune enlarged stencils in order to minimize transport anisotropy.

Keywords

transport; numerical diffusion; isotropy; mesh imprinting; modified equation;

Citations & Related Records

Reference

1	Bouche, D., Ghidaglia, J.-M. and Pascal, F. (2005), "Error estimate and the geometric corrector for the upwind finite volume method applied to the linear advection equation", SIAM J. Numer. Anal., 43(2), 578-603. https://doi.org/10.1137/040605941. DOI
2	Burton, D.E., Morgan, N.R., Carney, T.C., and Kenamond, M.A. (2015), "Reduction of dissipation in Lagrange cell-centered hydrodynamics (CCH) through corner gradient reconstruction (CGR)", J. Comput. Phys., 299, 229-280. https://doi.org/10.1016/j.jcp.2015.06.041. DOI
3	DeBar, R. (1974), "Fundamentals of the KRAKEN code", Report UCIR-17366, Lawrence Livermore National Laboratory. https://doi.org/10.2172/7227630.
4	Hamilton, B. and Bilbao, S. (2013), "On finite difference schemes for the 3-D wave equation using non-Cartesian grids", Proceedings of the Sound and Music Computing Conference, Stockholm, Sweden.
5	Hirt, C.W., Amsden, A.A., and Cook, J.L. (1974), "An arbitrary Lagrangian-Eulerian computing method for all flow speeds", J. Comput. Phys., 14(3), 227-253. https://doi.org/10.1016/0021-9991(74)90051-5. DOI
6	Kumar, A. (2004), "Isotropic finite-differences", J. Comput. Phys., 201(1), 109-118. https://doi.org/10.1016/j.jcp.2004.05.005. DOI
7	Lung, T.B. and Roe, P.L. (2012), "Toward a reduction of mesh imprinting", Int. J. Numer. Methods Fluids, 76(7), 450-470. https://doi.org/10.1002/fld.3941. DOI
8	Potter, M.E., Lamoureux, M., and Nauta, M.D. (2011), "An FDTD scheme on a face-centered-cubic (FCC) grid for the solution of the wave equation", J. Comput. Phys., 18, 53-80. https://doi.org/10.1016/j.jcp.2011.04.027.
9	Roe, P. (2017), "Multidimensional upwinding", Handbook of Numerical Analysis, 18, 53-80. https://doi.org/10.1016/bs.hna.2016.10.009.
10	Salmasi, M. and Potter, M. (2018), "Discrete exterior calculus approach for discretizing Maxwell's equations on face-centered cubic grids for FDTD", J. Comput. Phys., 364, 298-313. https://doi.org/10.1016/j.jcp.2018.03.019. DOI
11	Terekhov, K.M., Mallison, B.T., and Tchelepi, H.A. (2017), "Cell-centered nonlinear finite-volume methods for the heterogeneous anisotropic diffusion problem", J. Comput. Phys., 330, 245-267. https://doi.org/10.1016/j.jcp.2016.11.010. DOI
12	Warming, R.F. and Hyett, B.J. (1974), "The modified equation approach to the stability and accuracy analysis of finite-difference methods", J. Comput. Phys., 14(2), 159-179. https://doi.org/10.1016/0021-9991(74)90011-4. DOI
13	Zohuri B. (2017), "Inertial Confinement Fusion Driven Thermonuclear Energy", Springer. https://doi.org/10.1007/978-3-319-50907-5.
14	Vazquez-Gonzalez, T. (2016), "Conservative and mimetic numerical schemes for compressible multiphase flows simulation", Ph.D. dissertation, Universite Paris-Saclay, France. https://www.theses.fr/2016SACLC051.