Conservation Errors and Convergence Characteristics of Iterative Space-Marching Algorithms

Thompson, D., & Matus, R. (1991). Conservation Errors and Convergence Characteristics of Iterative Space-Marching Algorithms. AIAA Journal. Washington, DC: AIAA. 29(2), 227-234. DOI:10.2514/3.59917.

Abstract

The new iterative space-marching algorithms for numerical solution of the parabolized Navier-Stokes equations are critically examined. It is shown by analysis and numerical examples that employing parabolized flux difference splitting in the marching direction can lead to serious conservation errors even though a finite-volume formulation is employed. Schemes employing parabolized flux vector splitting in the marching direction are shown to be conservative. The structure of the iterative algorithm is examined to determine what factors play important roles in the convergence of the local iteration.