Finite volume methods on unstructured Voronoi meshes for hyperbolic conservation laws

被引：0

作者：

Christov, Ivan ^{[1
]}

Mishev, Ilya D. ^{[2
]}

Popov, Bojan ^{[3
]}

机构：

[1] Northwestern Univ, Dept Engn Sci & Appl Math, Evanston, IL 60208 USA

[2] ExxonMobil Upstream Res Co, Houston, TX 77252 USA

[3] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA

来源：

HYPERBOLIC PROBLEMS: THEORY, NUMERICS AND APPLICATIONS, PART 2 | 2009年 / 67卷

关键词：

Finite volume method; Non-oscillatory reconstruction; Voronoi mesh; Two-phase immiscible incompressible flow; SCHEMES;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We discuss the construction and convergence of high-resolution Godunov-type finite volume schemes for hyperbolic conservation laws on a class of unstructured polygonal meshes. In particular, we examine how reconstructions designed for unstructured triangulations can be extended to the more general Voronoi meshes. Finally, we apply the proposed high-resolution scheme to the equations of two-phase immiscible incompressible flow and ascertain the utility of the scheme for reservoir simulation.

引用

页码：507 / +

页数：2

共 50 条

[41] Hyperbolic conservation laws on manifolds. An error estimate for finite volume schemes
Philippe G. LeFloch
Baver Okutmustur
Wladimir Neves
Acta Mathematica Sinica, English Series, 2009, 25 : 1041 - 1066
[42] Optimal recovery using thin plate splines in finite volume methods for the numerical solution of hyperbolic conservation laws
Sonar, T
IMA JOURNAL OF NUMERICAL ANALYSIS, 1996, 16 (04) : 549 - 581
[43] The multi-dimensional limiters for solving hyperbolic conservation laws on unstructured grids II: Extension to high order finite volume schemes
Li, Wanai
Ren, Yu-Xin
JOURNAL OF COMPUTATIONAL PHYSICS, 2012, 231 (11) : 4053 - 4077
[44] Multi-dimensional Optimal Order Detection (MOOD) - a Very High-Order Finite Volume Scheme for Conservation Laws on Unstructured Meshes
Clain, S.
Diot, S.
Loubere, R.
FINITE VOLUMES FOR COMPLEX APPLICATIONS VI: PROBLEMS & PERSPECTIVES, VOLS 1 AND 2, 2011, 4 : 263 - +
[45] High order localized ENO schemes on unstructured meshes for conservation laws
Zhu, J
Zhao, N
Zheng, HS
MODERN PHYSICS LETTERS B, 2005, 19 (28-29): : 1563 - 1566
[46] Analysis of a class of spectral volume methods for linear scalar hyperbolic conservation laws
Lu, Jianfang
Jiang, Yan
Shu, Chi-Wang
Zhang, Mengping
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2024, 40 (06)
[47] The optimal convergence rate of monotone finite difference methods for hyperbolic conservation laws
Sabac, F
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1997, 34 (06) : 2306 - 2318
[48] Finite-difference methods for one-dimensional hyperbolic conservation laws
Berkenbosch, A.C.
Kaasschieter, E.F.
ten Thije Boonkkamp, J.H.M.
Numerical Methods for Partial Differential Equations, 1994, 10 (02) : 225 - 269
[49] Adaptive discontinuous Galerkin finite element methods for nonlinear hyperbolic conservation laws
Hartmann, R
Houston, P
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2002, 24 (03): : 979 - 1004
[50] Optimal convergence rate of monotone finite difference methods for hyperbolic conservation laws
SIAM J Numer Anal, 6 (2306-2318):

← 1 2 3 4 5 →