期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 304, 期 -, 页码 275-319出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2015.10.014
关键词
Path-conservative HLLEM Riemann solver; Resolution of linearly degenerate intermediate waves; Conservation laws and general hyperbolic; PDE with non-conservative terms; Well-balanced scheme for single and two-layer shallow water equations; Euler equations with real equation of state and multiphase flows; RMHD/MHD equations and nonlinear elasticity
资金
- European Research Council (ERC) under the European Union's Seventh Framework Programme (FP7) with the research project STiMulUs, ERC Grant [278267]
- NSF [NSF-AST-1009091, NSF-ACI-1307369, NSF-DMS-1361197, NSF-ACI-1533850]
- NASA grants from the Fermi program
- NASA-NNX [12A088G]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1622457] Funding Source: National Science Foundation
- Division of Computing and Communication Foundations
- Direct For Computer & Info Scie & Enginr [1533850] Funding Source: National Science Foundation
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1361197] Funding Source: National Science Foundation
In this paper a new, simple and universal formulation of the HLLEM Riemann solver (RS) is proposed that works for general conservative and non-conservative systems of hyperbolic equations. For non-conservative PDE, a path-conservative formulation of the HLLEM RS is presented for the first time in this paper. The HLLEM Riemann solver is built on top of a novel and very robust path-conservative HLL method. It thus naturally inherits the positivity properties and the entropy enforcement of the underlying HLL scheme. However, with just the slight additional cost of evaluating eigenvectors and eigenvalues of intermediate characteristic fields, we can represent linearly degenerate intermediate waves with a minimum of smearing. For conservative systems, our paper provides the easiest and most seamless path for taking a pre-existing HLL RS and quickly and effortlessly converting it to a RS that provides improved results, comparable with those of an HLLC, HLLD, Osher or Roe-type RS. This is done with minimal additional computational complexity, making our variant of the HLLEM RS also a very fast RS that can accurately represent linearly degenerate discontinuities. Our present HLLEM RS also transparently extends these advantages to non-conservative systems. For shallow water-type systems, the resulting method is proven to be well-balanced. Several test problems are presented for shallow water-type equations and two-phase flow models, as well as for gas dynamics with real equation of state, magnetohydrodynamics (MHD & RMHD), and nonlinear elasticity. Since our new formulation accommodates multiple intermediate waves and has a broader applicability than the original HLLEM method, it could alternatively be called the HLLI Riemann solver, where the I stands for the intermediate characteristic fields that can be accounted for. (C) 2015 Elsevier Inc. All rights reserved.
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