High-order finite volume schemes based on defect corrections

被引：3

作者：

Filimon, Alexander ^{[1
]}

Dumbser, Michael ^{[2
]}

Munz, Claus-Dieter ^{[1
]}

机构：

[1] Univ Stuttgart, D-70569 Stuttgart, Germany

[2] Univ Trento, I-38050 Trento, Italy

来源：

ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK | 2013年 / 93卷 / 6-7期

关键词：

Finite volume schemes; defect corrections; WENO reconstruction on unstructured meshes; high-order accuracy; advection diffusion reaction equations; steady state; ESSENTIALLY NONOSCILLATORY SCHEMES; UNSTRUCTURED MESHES; CONSTRUCTION;

D O I：

10.1002/zamm.201200007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For the approximation of steady state solutions, we propose an iterated defect correction approach to achieve higher-order accuracy. The procedure starts with the steady state solution of a low-order scheme, in general a second order one. The higher-order reconstruction step is applied a posteriori to estimate the local discretization error of the lower-order finite volume scheme. The defect is then used to iteratively shift the basic lower-order scheme to the desired higher-order accuracy given by the polynomial reconstruction. Hence, instead of solving the high-order discrete equations the low-order basic scheme is solved several times. This avoids that the high-order reconstruction with a large stencil has to be implemented into an existing basic solver and can be seen as a non-intrusive approach to higher-order accuracy.

引用

页码：423 / 436

页数：14