Unsteady, one-dimensional gas dynamics computations using a TVD type sequential solver

The efficacy of high resolution convection schemes in a sequential solution framework to resolve sharp gradients in unsteady, one-dimensional flows is investigated. It has been demonstrated in an earlier study that TVD schemes with special source term treatment can be effectively implemented in sequential solvers to resolve discontinuities in the flowfield by assigning the local convection speed as the characteristic speed for the whole sequential system of equations, thus coordinating the speed of signal propagation. Such a sequential approach is applied in this study to solve two unsteady flow problems-one involving the interaction of the various waves in a shock tube with closed reflecting ends and the other involving the unsteady gas dynamics in a tube with closed ends subject to an initial pressure perturbation (the resonant pipe problem). Procedures of source term treatment and a modified artificial compression strategy have also been devised to improve the performance of the scheme. These studies have identified the performance characteristics of the convection schemes in the sequential solution approach.