An Efficient Implicit TVD Method for Compressible Flow Simulations

The flow equations typically solved in two general techniques of explicit and implicit in density-based methods. Implementations of the flow solution algorithm for implicit methods are commonly more difficult than the explicit ones and for this reason, the flow simulations began with explicit procedures. The present paper describes an implementation of total variation diminishing (TVD) scheme into a density-based implicit finite-volume procedure with a simple flux linearization to solve the Euler and Navier–Stokes equations. The developed algorithm has three notable features: 1) using a simple linearization technique for implicit convective fluxes, 2) using a high-resolution TVD scheme to enhance the algorithm accuracy and 3) easy implementation of the algorithm compared to other implicit and explicit methods. Present implicit algorithm is based on an iterative procedure. For simplicity, all the equations are developed in two dimensional Cartesian coordinates. To solve equations set obtained from discretization, ADI method is used. Results show that the present procedure is accurate for a wide range of Mach numbers, so that it predicts shock waves and unsteady boundary layer with high accuracy for both steady and unsteady flows.