A mixed explicit-implicit splitting method for the compressible Navier-Stokes equations

Abstract

An application of both explicit and implicit operations in a time-splitting technique is carried out for viscous interaction studies between a laminar boundarylayer and an incident shock wave. The physical problem characterized by large local gradients near the wall demands a novel numerical technique that maintains accuracy and efficiency for stretched meshes. Specifically, the two-dimensional Navier-Stokes equations are solved by a sequence of one-dimensional operators, each being explicit or implicit for streamwise or normal coordinate operation, respectively. The explicit operator employs a non-centered scheme due to MacCormack. The implicit operator is of the Laasonen type and is second-order accurate for non-uniform spacing. Both the explicit and mixed splitting techniques are evaluated using selected experimental data. The mixed technique is more economical and is free of non-linear instabilities that plague the explicit one in the computation of extensive separated flows. Some discrepancies between the numerical and experimental results remain to be investigated as the theory tends to underpredict the size of the separation zone.