A Multi-material Five-equation-reduced Model and Artificial Compression Method for Interface Capture

doi:10.19596/j.cnki.1001-246x.8248

Abstract

Abstract:

The volume fraction equations of five-equation-reduced model were studied and numerical scheme was developed in two-dimensional Eulerian frame in planar and cylindrical geometry. To capture material interfaces, Yang's slope modification of artificial compression method was adopted in MUSCL, PPM and WENO type data reconstruction processes. HLLC-HLLCM hybrid flux was applied in Godunov type scheme to avoid numerical shock instability. For multi-material Riemann problems, numerical results show that the scheme captures shock and contact discontinuities with non-oscillatory character. No numerical shock instabilities growing shows as small perturbations was adding on initial physical variables. SOD problems in cylindrical and spherical geometries and contact-type two-dimensional Riemann problem were studied.

Key words: multi-material five-equation model, artificial compression method, HLLC-HLLCM hybrid flux, numerical shock instability

CLC Number:

Chuang XUE, Xingdong LI, Wenjun SUN, Wenhua YE, Xianjue PENG. A Multi-material Five-equation-reduced Model and Artificial Compression Method for Interface Capture[J]. Chinese Journal of Computational Physics, 2021, 38(3): 257-268.

Figures/Tables 8

Fig.1 Discontinuity states and wave structures of HLLC and HLLCM flux (a) discontinuity states for HLLC; (b) discontinuity states for HLLCM

Fig.2 Mesh interface and six neighbor-meshes for adjusting hybrid flux

Fig.3 Influence of mesh number and numerical method on contact discontinuity calculation (a) static contact discontinuity calculated by MUSCL; (b) moving contact discontinuity calculated by MUSCL; (c) moving contact discontinuity calculated by PPM; (d) moving contact discontinuity calculated by WENO

Fig.4 Profiles of density and volume fractions after two blast waves interaction (a) results of different schemes; (b) results of different models

Fig.5 Profile of density calculated by different numerical flux (a) density isolines calculated by HLLC-HLLCM flux; (b) density isolines calculated by HLLC flux; (c) profiles of density calculated by HLLC-HLLCM flux; (d) profiles of density calculated by HLLC flux

Fig.6 Profiles of density for cylindrical and spherical SOD problems with MUSCL+ACM+Hybrid scheme (a) 2D density contours for cylindrical SOD problem; (b) 2D density contours for spherical SOD problem; (c) 1D density profile for cylindrical SOD problem; (d) 1D density profile for spherical SOD problem

Fig.7 Profiles of density for cylindrical and spherical SOD problems with MUSCL+HLL scheme (a) 2D density contours for cylindrical SOD problem; (b) 2D density contours for spherical SOD problem; (c) 1D density profile for cylindrical SOD problem; (d) 1D density profile for spherical SOD problem

Fig.8 Density profile and material interfaces of 2D Riemann problems (a) density isolines without ACM; (b) density isolines with ACM; (c) four material interfaces without ACM; (d) four material interfaces with ACM

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