Further study on the geometric conservation law for finite volume method on dynamic unstructured mesh

Abstract Several common approaches to satisfy discretized geometry conservation law (DGCL) on dynamic unstructured mesh are reviewed and studied both analytically and numerically. According to different ways of eliminating DGCL error, these approaches are classified into two categories: the ‘volume-constrained’ method (VCM) with different source terms and the ‘face-constrained’ method (FCM) without any source term. Based on the error analysis, a unified form of VCMs is presented in this paper. The numerical results of typical test cases validate the geometric conservation property and the time-accuracy of FCMs, and illustrate the importance of the numerical scheme of face velocity for VCMs. Further theoretical study proves that the ‘Sweeping Volume Conservation Law’ (SVCL) could be a more stringent and appropriate condition than the traditional DGCL.