A class of compact upwind TVD difference schemes

A new method was proposed for constructing total variation diminishing (TVD) upwind schemes in conservation forms. Two limiters were used to prevent nonphysical oscillations across discontinuity. Both limiters can ensure the nonlinear compact schemes TVD property. Two compact TVD (CTVD) schemes were tested, one is third-order accuracy, and the other is fifth-order. The performance of the numerical algorithms was assessed by one-dimensional complex waves and Riemann problems, as well as a two-dimensional shock-vortex interaction and a shock-boundary flow interaction. Numerical results show their high-order accuracy and high resolution, and low oscillations across discontinuities.