A discrete geometric conservation law (DGCL) for a cell vertex finite-volume algorithm on moving domains

作者：Gil A J^*; Bonet J; Silla J; Hassan O

来源：International Journal for Numerical Methods in Biomedical Engineering, 2010, 26(6): 770-779.

DOI：10.1002/cnm.1180

• arbitrary Lagrangian-Eulerian formulation
• discrete geometric conservation law
• conservation equations

This paper revisits the classical discrete geometric conservation law for the arbitrary Lagrangian Eulerian conservation equations in a moving domain when the conservation laws are mapped to a fixed reference domain. The discretized form of the equations is formulated by means of a cell vertex finite-volume algorithm with special emphasis on the implications of the discrete time space algorithm for the preservation of free-stream flows. Under these circumstances, two corrections are introduced in order to guarantee the preservation of a free-stream flow evolving in time. A time correction is required to resolve the integration errors in the Jacobian of the transformation or mapping between fixed referential and current domains. A spatial correction is also needed to account for the inexact surface integration in the faces of the dual mesh.

• 出版日期2010-6