Shock capturing with Padé methods

摘要

A fourth order conservative Padé shock capturing method for conservation laws is developed and tested. Conservation is maintained by applying the primitive function reconstruction method developed by Shu and Osher for ENO schemes to a Padé method. In particular, we study a nonsymmetric Padé approximation that we have not seen before. Limiters are used to prevent spurious oscillations near shocks and a Runge-Kutta method is used to march the solution in time.Numerical experiments are performed to find limiters which maintain accuracy at smooth extrema, minimize spurious oscillations near shocks and resolve high frequency smooth solutions.