An Essentially Nonoscillatory High-Order Padé-Type (ENO-Padé) Scheme

A new, essentially nonoscillatory high-order Padé-type (ENO-Padé) scheme has been developed by incorporating the ENO interpolation algorithm into the cell-centered Padé scheme. The scheme is designed to eliminate the nonphysical oscillatory behavior of the Padé scheme across discontinuities and to improve the performance of the ENO scheme in smooth regions. The main features of the ENO-Padé scheme are illustrated by the solution of the scalar transport equation, while the extension of the method to the solution of compressible flow equations is also demonstrated. A number of numerical test cases, including two scalar-transport problems and three compressible flows, are used to compare the performances of the ENO-Padé scheme against other available schemes, such as upwind-biased, Padé, and ENO schemes. The numerical results show that the ENO-Padé scheme is an excellent compromise of the available schemes for resolving profiles over flow discontinuities while maintaining accurate flow structures in smooth regions.