000190481 001__ 190481
000190481 005__ 20190316235743.0
000190481 0247_ $$2doi$$a10.1016/j.jcp.2013.07.009
000190481 022__ $$a0021-9991
000190481 02470 $$2ISI$$a000323610500011
000190481 037__ $$aARTICLE
000190481 245__ $$aMulti-dimensional hybrid Fourier continuation-WENO solvers for conservation laws
000190481 269__ $$a2013
000190481 260__ $$bElsevier$$c2013
000190481 336__ $$aJournal Articles
000190481 520__ $$aWe introduce a multi-dimensional point-wise multi-domain hybrid Fourier-Continuation/WENO technique (FC-WENO) that enables high-order and non-oscillatory solution of systems of nonlinear conservation laws, and essentially dispersionless, spectral, solution away from discontinuities, as well as mild CFL constraints for explicit time stepping schemes. The hybrid scheme conjugates the expensive, shock-capturing WENO method in small regions containing discontinuities with the efficient FC method in the rest of the computational domain, yielding a highly effective overall scheme for applications with a mix of discontinuities and complex smooth structures. The smooth and discontinuous solution regions are distinguished using the multi-resolution procedure of Harten [A. Harten, Adaptive multiresolution schemes for shock computations, J. Comput. Phys. 115 (1994) 319-338]. We consider a WENO scheme of formal order nine and a FC method of order five. The accuracy, stability and efficiency of the new hybrid method for conservation laws are investigated for problems with both smooth and non-smooth solutions. The Euler equations for gas dynamics are solved for the Mach 3 and Mach 1.25 shock wave interaction with a small, plain, oblique entropy wave using the hybrid FC-WENO, the pure WENO and the hybrid central difference-WENO (CD-WENO) schemes. We demonstrate considerable computational advantages of the new FC-based method over the two alternatives. Moreover, in solving a challenging two-dimensional Richtmyer-Meshkov instability (RMI), the hybrid solver results in seven-fold speedup over the pure WENO scheme. Thanks to the multi-domain formulation of the solver, the scheme is straightforwardly implemented on parallel processors using message passing interface as well as on Graphics Processing Units (GPUs) using CUDA programming language. The performance of the solver on parallel CPUs yields almost perfect scaling, illustrating the minimal communication requirements of the multi-domain strategy. For the same RMI test, the hybrid computations on a single GPU, in double precision arithmetics, displays five- to six-fold speedup over the hybrid computations on a single CPU. The relative speedup of the hybrid computation over the WENO computations on GPUs is similar to that on CPUs, demonstrating the advantage of hybrid schemes technique on both CPUs and GPUs. (C) 2013 Elsevier Inc. All rights reserved.
000190481 6531_ $$aFourier continuation methods
000190481 6531_ $$aHigh-order WENO methods
000190481 6531_ $$aMulti-resolution 	methods
000190481 6531_ $$aConservation laws
000190481 6531_ $$aShock waves
000190481 6531_ $$aParallel and many core computation
000190481 700__ $$aShahbazi, Khosro
000190481 700__ $$0247428$$g232231$$aHesthaven, Jan S.
000190481 700__ $$aZhu, Xueyu
000190481 773__ $$j253$$tJournal of Computational Physics$$q209-225
000190481 8564_ $$uhttps://infoscience.epfl.ch/record/190481/files/JCP2532013.pdf$$zn/a$$s1534673$$yn/a
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000190481 917Z8 $$x232231
000190481 937__ $$aEPFL-ARTICLE-190481
000190481 970__ $$aShahbazi2013/MCSS
000190481 973__ $$rREVIEWED$$sPUBLISHED$$aOTHER
000190481 980__ $$aARTICLE