Point-wise hierarchical reconstruction for discontinuous Galerkin and finite volume methods for solving conservation laws

JOURNAL OF COMPUTATIONAL PHYSICS

卷:230

Article

Xu, Zhiliang¹  Liu, Yingjie²  Du, Huijing¹  Lin, Guang³  Shu, Chi-Wang⁴ 

[1] Univ Notre Dame, Dept Appl & Computat Math & Statist, Notre Dame, IN 46556 USA

[2] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

[3] Pacific NW Natl Lab, Computat Math Grp, Richland, WA 99352 USA

[4] Brown Univ, Div Appl Math, Providence, RI 02912 USA

关键词: Discontinous Galerkin method;    Finite volume method;    Limiter;    Hierarchical reconstruction;    Hyperbolic conservation laws;   

DOI  :  10.1016/j.jcp.2011.05.014

来源: Elsevier

【 摘 要 】

We develop a new hierarchical reconstruction (HR) method [17,28] for limiting solutions of the discontinuous Galerkin and finite volume methods up to fourth order of accuracy without local characteristic decomposition for solving hyperbolic nonlinear conservation laws on triangular meshes. The new HR utilizes a set of point values when evaluating polynomials and remainders on neighboring cells, extending the technique introduced in Hu, Li and Tang [9]. The point-wise HR simplifies the implementation of the previous HR method which requires integration over neighboring cells and makes HR easier to extend to arbitrary meshes. We prove that the new point-wise HR method keeps the order of accuracy of the approximation polynomials. Numerical computations for scalar and system of nonlinear hyperbolic equations are performed on two-dimensional triangular meshes. We demonstrate that the new hierarchical reconstruction generates essentially non-oscillatory solutions for schemes up to fourth order on triangular meshes. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free