Assessment of TVD schemes for inviscid and turbulent flow computation

A systematic study has been conducted to assess the performance of the TVD schemes for practical flow computation. The viewpoint adopted here is to treat the TVD schemes as a combination of the standard central difference scheme with numerical dissipation terms. The controlled amount of numerical dissipation modifies the computed fluxes to ensure that the solution is oscillation‐free. Four variants of TVD schemes, two with upwind dissipation terms and two with symmetric dissipation terms, have been studied and compared with the conventional Beam‐Warming scheme for inviscid and turbulent axisymmetric flow computations. The results obtained show that all four variants can accurately resolve the shock and flow profiles with fewer grid points than the Beam‐Warming scheme. The convergence rates of the TVD schemes are also substantially superior to that of the Beam‐Warming scheme. The combination of high accuracy, good robustness and improved computational efficiency offered by the TVD schemes makes them attractive for computing high‐speed flow with shocks. In terms of the relative performances it is found that the symmetric schemes converge slightly faster but that the upwind schemes are less sensitive to the number of grid points being employed.