High-order localized dissipation weighted compact nonlinear scheme for shock- and interface-capturing in compressible flows

Wong, Man Long; Lele, Sanjiva K.

doi:10.1016/j.jcp.2017.03.008

Cited by 89 publications

(82 citation statements)

References 47 publications

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“…The parallelization of the code and all the construction, management, and storage of cells are facilitated by the Structured Adaptive Mesh Refinement Application Infrastructure (SAMRAI) library [32][33][34][35][36] from Lawrence Livermore National Laboratory (LLNL). Explicit form of sixth order localized dissipation weighted compact nonlinear scheme (WCNS) [37], which is designed to add sufficient dissipation around shocks and regions with large gradients for numerical stability and minimum dissipation in smooth regions to capture vortical features, is used for the hyperbolic part of the governing equations. Explicit sixth order finite differences are used to compute the derivatives of diffusive and viscous fluxes in non-conservative form.…”

Section: Methodsmentioning

confidence: 99%

“…F v , G v , and H v are the diffusive or viscous flux vectors in the x, y, and z directions. The explicit form of a sixth order weighted compact nonlinear scheme (WCNS) with nonlinear interpolation and approximate Riemann solver [37] is used to approximate the derivatives of the convective fluxes. The scheme is based on the sixth order accurate explicit midpoint-and-node-to-node differencing (MND) by Nonomura and Fujii [76].…”

Section: Appendix D: Spatial Discretizationsmentioning

confidence: 99%

“…whereF i+ 1 2 ,j,k are fluxes approximated at midpoints between cell nodes by the sixth order accurate nonlinear localized dissipation interpolation and hybrid Riemann solver given by Wong and Lele [37]. F i,j,k are the fluxes at cell nodes and ∆x is the uniform grid spacing in the x direction.…”

Section: Appendix D: Spatial Discretizationsmentioning

confidence: 99%

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High-resolution Navier-Stokes simulations of Richtmyer-Meshkov instability with reshock

2019

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The interaction of a Mach 1.45 shock wave with a perturbed planar interface between sulphur hexafluoride and air is studied through high-resolution two-dimensional (2D) and three-dimensional (3D) shock-capturing adaptive mesh refinement simulations of multi-species Navier-Stokes equations. The sensitivities of time-dependent statistics on grid resolution for 2D and 3D simulations are evaluated to ensure the accuracy of the results. The numerical results are used to examine the differences between the development of 2D and 3D Richtmyer-Meshkov instability during two different stages: (1) initial growth of hydrodynamic instability from multi-mode perturbations after first shock and (2) transition to chaotic or turbulent state after re-shock. The effects of the Reynolds number on the mixing in 3D simulations are also studied through varying the transport coefficients. * wongml@stanford.edu † livescu@lanl.gov ‡

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Section: Methodsmentioning

confidence: 99%

Section: Appendix D: Spatial Discretizationsmentioning

confidence: 99%

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High-resolution Navier-Stokes simulations of Richtmyer-Meshkov instability with reshock

2019

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“…The interpolation can be either explicit or implicit in space, also known as compact schemes. Details of the implementation of nonlinear interpolation schemes (WCNS) [34,43] are given in Appendix A. Compact linear interpolation polynomials, denoted as U-5C, for the left and right interface are as follows,…”

Section: Overview Of Upwind Finite Difference Schemesmentioning

confidence: 99%

First order hyperbolic approach for Anisotropic Diffusion equation

Chamarthi

Nishikawa

Komurasaki

2019

Journal of Computational Physics

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In this paper, we present a high order finite difference solver for anisotropic diffusion problems based on the first-order hyperbolic system method. In particular, we demonstrate that the construction of a uniformly accurate fifth-order scheme that is independent of the degree of anisotropy is made straightforward by the hyperbolic method with an optimal length scale. We demonstrate that the gradients are computed simultaneously to the same order of accuracy as that of the solution variable by using weight compact finite difference schemes. Furthermore, the approach is extended to improve further the simulation of the magnetized electrons test case previously discussed in Refs. [J. Comput. Phys., 284 (2015) 59-69 and 374 (2018) 1120-1151]. Numerical results indicate that these schemes are capable of delivering high accuracy and the proposed approach is expected to allow the hyperbolic method to be successfully applied to a wide variety of linear and nonlinear problems with anisotropic diffusion.

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“…In addition, shock-bubble interactions have also been widely used as a canonical reference system to test and scrutinise new numerical schemes, see e.g. (Allaire et al, 2002;Chang and Liou, 2007;Denner et al, 2018;Hu and Khoo, 2004;Kokh and Lagoutière, 2010;Nourgaliev et al, 2006;Saurel and Abgrall, 1999;Shukla, 2014;Shukla et al, 2010;Terashima and Tryggvason, 2009;Wong and Lele, 2017).…”

Section: Introductionmentioning

confidence: 99%

Numerical modelling of shock-bubble interactions using a pressure-based algorithm without Riemann solvers

Denner

Wachem

2019

Exp. Comput. Multiph. Flow

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The interaction of a shock wave with a bubble features in many engineering and emerging technological applications, and has been used widely to test new numerical methods for compressible interfacial flows. Recently, density-based algorithms with pressure-correction methods as well as fully-coupled pressure-based algorithms have been established as promising alternatives to classical density-based algorithms based on Riemann solvers. The current paper investigates the predictive accuracy of fully-coupled pressure-based algorithms without Riemann solvers in modelling the interaction of shock waves with one-dimensional and two-dimensional bubbles in gas-gas and liquid-gas flows. For a gas bubble suspended in another gas, the mesh resolution and the applied advection schemes are found to only have a minor influence on the bubble shape and position, as well as the behaviour of the dominant shock waves and rarefaction fans. For a gas bubble suspended in a liquid, however, the mesh resolution has a critical influence on the shape, the position and the post-shock evolution of the bubble, as well as the pressure and temperature distribution.

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High-order localized dissipation weighted compact nonlinear scheme for shock- and interface-capturing in compressible flows

Cited by 89 publications

References 47 publications

High-resolution Navier-Stokes simulations of Richtmyer-Meshkov instability with reshock

High-resolution Navier-Stokes simulations of Richtmyer-Meshkov instability with reshock

First order hyperbolic approach for Anisotropic Diffusion equation

Numerical modelling of shock-bubble interactions using a pressure-based algorithm without Riemann solvers

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