Demonstration of a Multi-Dimensional Time-Accurate Local Time Stepping CESE Method

Abstract

An improved time-accurate local time stepping space-time Conservation Element and Solution Element (CESE) method is demonstrated in this paper. The existing method is not applicable for a general unstructured mesh where fractional local time step size ratios among neighbor cells hinder a consistent procedure for solution synchronization. The current paper proposes a procedure which regularizes the local time step sizes whose ratios become dyadic integers or reciprocals of dyadic integers such that a local time stepping solution procedure can be synchronized at exact common time levels among neighbored cells. The resulting grid Courant numbers are bounded by one to two times a given global Courant number; the numerical condition is similar among all solution cells so the method assures solution quality uniformity throughout a solution domain. The proposed time step size regularization procedure is generally applicable for 1-D, 2-D, and 3-D meshes. This work also includes benchmark aeroacoustic and unsteady aerodynamic demonstration problems from which the improved local time stepping method is consistently proved to be robust for nonuniform unstructured meshes and still retain the high-resolution nature of the CESE method.