The normalized weighting factor method: A novel technique for accelerating the convergence of high-resolution convective schemes

This article deals with the development of a new method for accelerating the solution of flow problems discretized using high-resolution convective schemes. The technique is based on the normalized variable and space formulation (NVSF) methodology and is denoted here by the normalized weighting-factor (NWF) method. In contrast with the well-known deferred-correction (DC) procedure, the NWF method is fully implicit and is derived by directly replacing the control-volume face values by their functional relationships in the discretized equation. The direct substitution is performed by the introduction of a variable, NWF, that accounts for the multiplicity of interpolation profiles in HR schemes. The new method is compared with the widely used DC procedure and is shown to be, on average, four times faster.