Properties of blended advection schemes for hyperbolic conservation laws

The fidelity of an advection-dominant numerical solution is significantly affected by the order of approximation applied for the given scalar. Numerical schemes that apply this approximation are generally prone to dissipative and dispersive errors while capturing sharp discontinuities in the scalar values. Hence, the present study introduces the Fromm-scheme-based blending formulation for two blended schemes that demonstrate the accuracy and monotonicity while capturing the discontinuity in the numerical solution. The present study demonstrates the spectral analysis for the stability and accuracy of these blended schemes. The proposed blended schemes are applied to the pure advection problems and are compared to their constituent higher-order schemes and other blended schemes. Furthermore, these schemes are also applied over the lid driven cavity and one-dimensional dam break problems to estimate their performance over an unknown velocity field.