可压缩多介质流动问题的高精度数值模拟方法

何志伟; 田保林; 李理; 李海锋; 张又升; 孟宝清

doi:10.7638/kqdlxxb-2020.0165

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可压缩多介质流动问题的高精度数值模拟方法

专栏——计算流体力学高精度格式及其应用 | 更新时间：2026-05-28

- 可压缩多介质流动问题的高精度数值模拟方法
- High-order numerical simulation method for compressible multi-material flow problems
- 空气动力学学报 2021年39卷第1期页码：177-190
- 作者机构：
  
  1. 北京应用物理与计算数学研究所,北京,100094
  2. 北京大学应用物理与技术研究中心,北京,100871
- 作者简介：
  
  何志伟(1985-), 男, 江苏泗洪人, 副研究员, 研究方向: 计算流体力学.E-mail: he_zhiwei@iapcm.ac.cn
  田保林(1975-), 男, 山东成武人, 研究员, 研究方向: 湍流混合, 计算流体力学.E-mail: tian_baolin@iapcm.ac.cn
- 基金信息：
  
  国家自然科学基金青年科学基金项目（11702029）;国家自然科学基金重点项目（91852207）;国家自然科学基金联合基金项目（U1730111）;中国工程物理研究院院长基金（YZJJLX2018012）;国家重大项目National key project（GJXM92579）
- DOI：10.7638/kqdlxxb-2020.0165
  中图分类号： O-03-0359
- 纸质出版：2021
- 稿件说明：
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何志伟, 田保林, 李理, 李海锋, 张又升, 孟宝清. 可压缩多介质流动问题的高精度数值模拟方法[J]. 空气动力学学报, 2021, 39(1): 177-190.

HE Zhiwei, TIAN Baolin, LI Li, et al. High-order numerical simulation method for compressible multi-material flow problems[J]. 2021, 39(1): 177-190.
何志伟, 田保林, 李理, 李海锋, 张又升, 孟宝清. 可压缩多介质流动问题的高精度数值模拟方法[J]. 空气动力学学报, 2021, 39(1): 177-190. DOI： 10.7638/kqdlxxb-2020.0165.

HE Zhiwei, TIAN Baolin, LI Li, et al. High-order numerical simulation method for compressible multi-material flow problems[J]. 2021, 39(1): 177-190. DOI： 10.7638/kqdlxxb-2020.0165.

摘要

在可压缩流动问题的数值模拟领域，激波的高分辨率计算已取得重要进展。但是包含物质界面的可压缩多介质流动的数值模拟还存在诸多数值挑战，主要表现为界面处数值耗散过大和非物理振荡等问题。界面处流体性质的不连续性是造成可压缩多介质流动问题物理建模与数值方法困难的主要原因。为了建立一套高效的可压缩多介质流动问题的高精度数值模拟方案，本文从数值框架的选择、非守恒方程相容离散、高精度有界格式构造、界面压缩、界面-单介质分区计算方法等多个维度出发，综述近几年我们在可压缩多介质流动问题高精度数值模拟方法方面的研究进展。通过上述多个维度的工作，我们建立了一套适用于可压缩多介质流动问题的低耗散、基本无数值振荡的高精度欧拉数值方法，并成功应用于可压缩多介质大变形流动和界面不稳定性诱导湍流混合等问题的数值模拟。相关数值方法研究成果已集成至武器物理等领域工程数值模拟软件中，为相关工程任务提供了重要技术支撑。

Abstract

In the field of numerical simulation of compressible flows

significant progress has been made in high-resolution shock-capturing schemes. But there are still many numerical challenges in the numerical simulation of compressible multi-material flows involving material interfaces

which are mainly manifested by excessively numerical dissipation and non-physical oscillations across interfaces. The discontinuity of fluid properties at the interface is the main reason for the difficulty of physical modelling and numerical simulating of compressible multi-material flows. To establish an efficient and high-order numerical algorithm for such flows

five aspects must be considered simultaneously

i.e.

the numerical framework

the compatible discretization of non-conservative equations

the high-order bounded scheme

the interface-compression

and the multi-region calculation. In this paper we review our works in recent years from these aspects. Through the above-mentioned work

a class of high-order Eulerian numerical simulation methods with low dissipation and essentially non-oscillatory property has been established and successfully applied to interfacial instability and turbulent mixing of compressible multi-material fluids. These numerical methods have been integrated into numerical simulation softwares for engineering problems in weapon physics

and have been providing important technical support for related engineering tasks.

关键词

Keywords

references

LUND H. A hierarchy of relaxation models for two-phase flow[J]. SIAM Journal on Applied Mathematics, 2012(72): 1713-1741.

SAUREL R, PETITPAS F, BERRY. A simple and efficient relaxation methods for interfaces separating compressible fluids, cavitating flows and shocks in multiphase mixtures[J]. Journal of Computational Physics, 2009, 228: 1678-1712.

ABGRALL R. How to prevent pressure oscillations in multicomponent flow calculations: A quasi conservative approach[J]. Journal of Computational Physics, 1996, 125: 150-160.

SAUREL R, ABGRALL R. A simple method for compressible multifluid flows[J]. SIAM Journal on Scientific Computing, 1999, 21: 1115-1145.

SHYUE K. An effcient shock-capturing algorithm for compressible multicomponent problems[J]. Journal of Computational Physics, 1998, 142: 208-242.

DREW D. Mathematical modeling of two-phase flow[J]. Annual Review of Fluid Mechanics, 1983, 15: 261-291.

BAER M, NUNZIATO J. A two-phase mixture theory for the deflagration-to-detonation transition (DDT) in reactive granular materials[J]. International Journal of Multiphase Flows, 1986, 12: 861-889.

SAUREL R, ABGRALL R. A multiphase Godunov method for compressible multifluid and multiphase flows[J]. Journal of Computational Physics, 1999, 150: 425-467.

TIAN B, ZENG J, MENG B, et al. Compressible multiphase particle-in-cell method (CMP-PIC) for full pattern flows of gas-particle system[J]. Journal of Computational Physics, 2020, 418: 109602.

ANDRIANOV N, WARNECKE G. The Riemann problem for the Baer-Nunziato two-phase flow model[J]. Journal of Computational Physics, 2004, 195: 434-464.

HE Z, ZHANG Y, LI X, et al. Preventing numerical oscillations in the flux-split based finite difference method for compressible flows with discontinuities, Ⅱ[J]. International Journal for Numerical Methods in Fluids, 2016, 80: 306-316.

HE Z, ZHANG Y, LI X, et al. Preventing numerical oscillations in the flux-split based finite difference method for compressible flows with discontinuities[J]. Journal of Computational Physics, 2015, 300: 269-287.

JIANG G, SHU C W. Efficient implementation of weighted ENO schemes[J]. Journal of Computational Physics, 1996, 126: 202-228.

STEGER J L, WARMING R F. Flux vector splitting of the inviscid gas dynamic equations with applications to finite difference methods[J]. Journal of Computational Physics, 1981, 40: 263-293.

HE Z, LI L, ZHANG Y, et al. Consistent implementation of characteristic flux-split based finite difference method for compressible multi-material gas flows[J]. Computers and Fluids, 2018, 168: 190-200.

TORO E. Riemann solvers and numerical methods for fluid dynamics[M]. Springer, Berlin, 1999

JOHNSEN E. Implementation of WENO schemes in compressible multicomponent flow problems[J]. Journal of Computational Physics, 2006, 219: 715-732.

DENG X, ZHANG H. Developing high-order weighted compact nonlinear schemes[J]. Journal of Computational Physics, 2000, 165: 22-44.

HE Z, GAO F, TIAN B, LI J. Implementation of finite difference weighted compact nonlinear schemes with the two-stage fourth-order accurate temporal discretization[J]. Communications in Computational Physics, 2020, 27: 1470-1484.

NONOMURA T, MORIZAWA S, TERASHIMA H, et al. Numerical (error) issues on compressible multicomponent flows using a high-order differencing scheme: weighted compact nonlinear scheme[J]. Journal of Computational Physics, 2012, 231: 3181-3210.

MURRONE A, GUILLARD H. A five equation reduced model for compressible two phase flow problems[J]. Journal of Computational Physics, 2005, 202: 664-698.

HENRICK A, ASLAM T, POWERS J. Mapped weighted-essentially-non-oscillatory schemes: achieving optimal order near critical points[J]. Journal of Computational Physics, 2005, 207: 542-567.

BORGES R, CARMONA M, COSTA B, et al. An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws[J]. Journal of Computational Physics, 2008, 227: 3191-3211.

FU L, HU X, ADAM N. A family of high-order targeted ENO schemes for compressible-fluid simulations[J]. Journal of Computational Physics, 2016, 305: 333-359.

REN Y, LIU M, ZHANG H. A characteristic-wise hybrid compact-WENO scheme for solving hyperbolic conservation laws[J]. Journal of Computational Physics, 2003, 192: 365-386.

HE Z, LI X, LIANG X. Nonlinear spectral-like schemes for hybrid schemes[J]. Science China Physics, Mechanics and Astronomy, 2014, 57: 753-763.

SURESH A, HUYNH H. Accurate monotonicity-preserving schemes with Runge-Kutta time stepping[J]. Journal of Computational Physics, 1997, 136: 83-99.

HE Z, LI X, FU D, MA Y. A 5th order monotonicity-preserving upwind compact difference scheme[J]. Science China Physics, Mechanics and Astronomy, 2011, 54: 511-522.

BALSARA D, SHU C W. Monotonicity preserving WENO schemes with increasingly high-order of accuracy[J]. Journal of Computational Physics, 2000, 160: 405-452.

HE Z, ZHANG Y, GAO F, et al. An improved accurate monotonicity-preserving scheme for the Euler equations[J]. Computers and Fluids, 2016, 140: 1-10.

HA C, LEE J. A modified monotonicity-preserving high-order scheme with application to computation of multi-phase flows[J]. Computers and Fluids, 2020, 197: 104345.

ZHANG X, SHU C W. Maximum-principle-satisfying and positivity-preserving high-order schemes for conservation laws: survey and new developments[J]. Proc Roy Soc A, 2011, 467: 2752-76.

CLAIN S, DIOT S, LOUBERE R. A high-order finite volume method for systems of conservation laws-multi-dimensional optimal order detection(MOOD)[J]. Journal of Computational Physics, 2011, 230: 4028-4050.

SHUKLA R. Nonlinear preconditioning for efficient and accurate interface capturing in simulation of multicomponent compressible flows[J]. Journal of Computational Physics, 2014, 276: 508-540.

HE Z, TIAN B, ZHANG Y, et al. Characteristic-based and interface-sharpening algorithm for high-order simulations of immiscible compressible multi-material flows[J]. Journal of Computational Physics, 2017, 333: 247-268.

SHYUE K, XIAO F. An Eulerian interface sharpening algorithm for compressible two-phase flow: the algebraic THINC approach[J]. Journal of Computational Physics, 2014, 268: 326-354.

XIAO F, Ⅱ S, CHEN C. Revisit to the THINC scheme: a simple algebraic VOF algorithm[J]. Journal of Computational Physics, 2011, 230: 7086-7092.

ALLAIRE G, CLERC S, KOKN S. A five-equation model for the simulation of interfaces between compressible fluids[J]. Journal of Computational Physics, 2002, 181: 577-616.

KAPILA A, MENIKOFF R, BDZIL J, et al. Two-phase modeling of deflagration-to-detonation transition in granular materials: reduced equations[J]. Physics of Fluids, 2001, 13: 3002-3024.

HE Z, RUAN Y, YU Y, et al. Self-adjusting steepness based schemes that preserve discontinuous structures in compressible flows[J]. Journal of Computational Physics, 2021. (submitted)

TIWARI A, FREUND J, PANTANO C. A diffuse interface model with immiscibility preservation[J]. Journal of Computational Physics, 2013, 252: 2900-309.

LI L, CHEN Q, TIAN B. Transport diffuse interface model for simulation of solid-fluid interaction[J]. Applied Mathematics and Mechanics-English Edition, 2019, 40: 321-330.

LI L, CHEN Q, HE Z, et al. An improved pressure-equilibrium diffuse interface model for solid-fluid interaction[J]. Communications in Computational Physics, 2020, 27: 546-568.

LI H, HE Z, ZHANG Y, et al. On the role of rarefaction/compression waves in Richtmyer-Meshkov instability with reshock[J]. Physics of Fluids, 2019, 31: 054102.

HU Z, ZHANG Y, TIAN B. Evolution of Rayleigh-Taylor instability under interface discontinuous acceleration induced by radiation[J]. Physical Review E, 2020, 101: 043115.

GAO F, ZHANG Y, HE Z, et al. Formula for growth of mixing width applied to Richtmyer-Meshkov instability[J]. Physics of Fluids, 2016, 28: 114101.

DAL MASO G, LEFLOCH P, MURAT F. Definition and weak stability ofnoncon-servative product[J]. Journal de Mathématiques Pures et Appliqués, 1995, 74: 483-548.

PARES C. Numerical methods fornonconservative hyperbolic systems: A theoretical framework[J]. SIAM Journal on Numerical Analysis, 2006, 44: 300-321

DUMBSER M, HIDALGO A, CASTRO M, et al. FORCE schemes on unstructured meshes Ⅱ: Non-conservative hyperbolic systems[J]. Computer Methods in Applied Mechanics and Engineering, 2010, 199: 625-647.

ABGRALL R, KARNI S. A comment on the computation of non-conservative products[J]. Journal of Computational Physics, 2010, 229: 2759-2763.

KOKH S, LAGOUTIERE F. An anti-diffusive numerical scheme for the simulation of interfaces between compressible fluids by means of a five-equation model[J]. Journal of Computational Physics, 2010, 229: 2773-2809.

SO K, HU X, ADAMS N. Anti-diffusion interface sharpening technique for two-phase compressible flow simulations[J]. Journal of Computational Physics, 2012, 231: 4304-4323.

OLSSON E, KREISS G, ZAHEDI S. A conservative level set method for two phase flow, Ⅱ[J]. Journal of Computational Physics, 2007, 225: 785-807.

CHIU P, LIN Y. A conservative phase field method for solving incompressible two-phase flows[J]. Journal of Computational Physics, 2011, 230: 185-204.

JAIN S, MANI A, MOIN P. A conservative diffuse-interface method for compressible two-phase flows[J]. Journal of Computational Physics, 2020, 418: 109606.

PERIGAUD G, SAUREL R. A compressible flow model with capillary effects[J]. Journal of Computational Physics, 2005, 209: 139-178.

CARALIC V, COLONIUS T. Finite-volume WENO scheme for viscous compressible multicomponent flows[J]. Journal of Computational Physics, 2014, 274: 95-121.

THORNBER B, GROOM M, YOUNGS D. A five-equation model for the simulation of miscible and viscous compressible fluids[J]. Journal of Computational Physics, 2018, 372: 256-280.

JOHNSEN E, HAM F. Preventing numerical errors generated by interface-capturing schemes in compressible multi-material flows[J]. Journal of Computational Physics, 2012, 231: 5705-5717.

SAUREL R, PANTANO C. Diffuse-interface capturing methods for compressible two-phase flows[J]. Annual Review of Fluid Mechanics, 2018, 50: 105-30.

FAVRIE N, GAVRILYUK S. Diffuse interface model for compressible fluid-compressible elastic-plastic solid interaction[J]. Journal of Computational Physics, 2012, 231: 2695-2723.

NDANOU S, FAVRIE N, GAVRILYUK S. Multi-solid and multi-fluid diffuse interface model: Applications to dynamic fracture and fragmentation[J]. Journal of Computational Physics, 2015, 295: 523-555.

HOWELL L, GREENOUGH J. Radiation diffusion for multi-fluid Eulerian hydrodynamics with adaptive mesh refinement[J]. Journal of Computational Physics, 2003, 184: 53-78.

DENG X, SHIMIZU Y, XIAO F. A fifth-order shock capturing scheme with two-stage boundary variation diminishing algorithm[J]. Journal of Computational Physics, 2019, 386: 323-349.

DENG X, JIANG Z, XIAO F, et al. Implicit large eddy simulation of compressible turbulence flow with PnTm-BVD scheme[J]. Applied Mathematical Modelling, 2020, 77: 17-31.

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