1. Compact high order finite volume method on unstructured grids IV: Explicit multi-step reconstruction schemes on compact stencil
- Author
-
Qian Wang, Yu-Xin Ren, and Yu-Si Zhang
- Subjects
finite volume methods ,Physics and Astronomy (miscellaneous) ,Computer science ,010103 numerical & computational mathematics ,01 natural sciences ,spectral difference method ,Continuation ,efficient implementation ,Quadratic equation ,Discontinuous Galerkin method ,0101 mathematics ,unstructured grids ,Reconstruction procedure ,discontinuous galerkin method ,Numerical Analysis ,Conservation law ,essentially nonoscillatory schemes ,Finite volume method ,hybrid dg/fv methods ,Computer simulation ,Compact stencil ,Applied Mathematics ,incompressible flows ,element-method ,numerical-simulation ,Computer Science Applications ,010101 applied mathematics ,high order schemes ,Computational Mathematics ,multidimensional limiters ,Modeling and Simulation ,multi-step reconstruction ,Algorithm ,conservation-laws - Abstract
In the present paper, a multi-step reconstruction procedure is proposed for high order finite volume schemes on unstructured grids using compact stencil. The procedure is a recursive algorithm that can eventually provide sufficient relations for high order reconstruction in a multi-step procedure. Two key elements of this procedure are the partial inversion technique and the continuation technique. The partial inversion can be used not only to obtain lower order reconstruction based on existing reconstruction relations, but also to regularize the existing reconstruction relations to provide new relations for higher order reconstructions. The continuation technique is to extend the regularized relations on the face-neighboring cells to current cell as additional reconstruction relations. This multi-step procedure is operationally compact since in each step only the relations defined on a compact stencil are used. In the present paper, the third and fourth order finite volume schemes based on two-step quadratic and three-step cubic reconstructions are studied. (C) 2019 Elsevier Inc. All rights reserved.
- Published
- 2019