Solution acceleration for steady flow using the Conservation Element and Solution Element (CE/SE) method

Abstract

The method of Space-Time Conservation Element and Solution Element (CE/SE) is a high-resolution and multidimensional numerical method for solving conservation laws. The CE/SE's unique feature is that both space and time are unified and treated as a single entity, and both local and global flux conservation in space and time is enforced. The method avoids the limitations of the traditional approaches to capture the physics more efficiently and realistically. The scheme being an explicit time stepping method is intended for time dependent problems and thus makes considerable demands on the computing requirements for steady state flow solutions. To overcome this difficulty, traditional techniques used to accelerate the convergence of flows to a steady state are considered in this paper. The methods used for explicit flow solvers, namely multigrid, enthalpy damping, and local time stepping, are applied in the context of the CE/SE method. The accuracy and efficiency of the techniques are verified by Euler calculations for a range of test problems in two dimensions. The capabilities of the methods are assessed individually and collectively. Results show that the computational efficiency for the CE/SE can be realized. © 2003 by by the authors.