A high-wavenumber viscosity for high-resolution numerical methods

A spectral-like viscosity is proposed for centered differencing schemes to help stabilize numerical solutions and reduce oscillations near discontinuities. Errors introduced by the added dissipation can be made arbitrarily small by adjusting the power of the derivative in the viscosity term. The high-wavenumber viscosity is combined with a 10th-order compact scheme to produce an accurate and efficient shock-capturing method. The new scheme compares favorably with other shock-capturing algorithms.