Low dispersion and boundedness practical discretization scheme

This paper presents an effective discretization scheme for approximating convective transport. The discretization scheme, the weighted second upwind and central differencing (WSUC) scheme, uses weighted second order upwind and central differencing. The theoretical analysis shows that the WSUC scheme is total variation bounded and unconditionally stable for convective numerical stability. Two numerical tests show that the WSUC scheme is more accurate and has higher resolution than the first order upwind scheme, a second order upwind scheme, the SOUCUP scheme and the MSOUCUP scheme. As an example, the thermal stratification in a thermal storage tank is calculated using the WSUC scheme.