A study of dispersion-relation-preserving and optimized prefactored compact schemes for wave equations

In the present study, the Dispersion-Relation-Preserving (DRP) scheme by Tam and coworkers, and the optimized prefactored compact (OPC) scheme by Ashcroft and Zhang, are assessed. The original schemes are developed in the finite difference framework; in the present effort, their corresponding finite volume versions are developed. Both DRP and OPC schemes, based on either finite difference or finite volume approach, attempt to optimize the coefficients for high resolution of short waves with respect to the computational grid while maintaining pre-determined formal orders of accuracy. Highlighting the principal characteristics of the schemes and utilizing simple linear and nonlinear wave equations with different wavelengths as the test cases, the performance of these approaches is documented. For the linear wave equation, there is no major difference between the DRP and OPC schemes. For the nonlinear wave equations, the finite volume version of both DRP and OPC schemes again perform comparably, and offer substantially better solutions in regions of high gradient or discontinuity.