On Further Development of an Unstructured Space-Marching Technique

Abstract

Space marching methods are widely used to calculate steady supersonic internal and external flows in view of their superior efficiency as compared to time marching approaches. A very general space-marching procedure was proposed by Nakahashi and Saitoh in 1996. The method can be used with any explicit time-marching procedure, allows for embedded subsonic regions, and is well-suited for unstructured grids, enabling a maximum of geometric flexibility. The flow field is only updated in the so-called active domain. Once the residual has fallen below a preset tolerance, the active domain is shifted. The present work is aimed at further refining of the Nakahashi and Saitoh’s method. This is achieved via the following new approaches: (a) A non-reflecting boundary condition is implemented at the exit of the active domain, thus eliminating non-physical reflections propagating upstream; (b) A general, user-independent procedure for partitioning of the computational domain into a set of active domains is proposed. These allow to minimize the size of the active domain and the residual monitor region, thus contributing to the method’s efficiency; (c) Local grid adaptation is performed in the course of space marching. These ideas are verified and tuned, at first, on two simple test problems (supersonic flows over compression and expansion corners). Finally, the results of the application of the improved method to supersonic flows in air-breathing engine inlets and ram accelerators are presented.