Showing papers by "Mark H. Carpenter published in 1998"

Computational Considerations for the Simulation of Shock-Induced Sound

Abstract: The numerical study of aeroacoustic problems places stringent demands on the choice of a computational algorithm because it requires the ability to propagate disturbances of small amplitude and short wavelength. The demands are particularly high when shock waves are involved because the chosen algorithm must also resolve discontinuities in the solution. The extent to which a high-order accurate shock-capturing method can be relied upon for aeroacoustics applications that involve the interaction of shocks with other waves has not been previously quantified. Such a study is initiated in this work. A fourth-order accurate essentially nonoscillatory (ENO) method is used to investigate the solutions of inviscid, compressible flows with shocks. The design order of accuracy is achieved in the smooth regions of a steady-state, quasi-one-dimensional test case. However, in an unsteady test case, only first-order results are obtained downstream of a sound-shock interaction. The difficulty in obtaining a globally high-order accurate solution in such a case with a shock-capturing method is demonstrated through the study of a simplified, linear model problem. Some of the difficult issues and ramifications for aeroacoustic simulations of flows with shocks that are raised by these results are discussed.

Higher-Order Compact Schemes for Numerical Simulation of Incompressible Flows

Abstract: A higher order accurate numerical procedure has been developed for solving incompressible Navier-Stokes equations for 2D or 3D fluid flow problems It is based on low-storage Runge-Kutta schemes for temporal discretization and fourth and sixth order compact finite-difference schemes for spatial discretization The particular difficulty of satisfying the divergence-free velocity field required in incompressible fluid flow is resolved by solving a Poisson equation for pressure It is demonstrated that for consistent global accuracy, it is necessary to employ the same order of accuracy in the discretization of the Poisson equation Special care is also required to achieve the formal temporal accuracy of the Runge-Kutta schemes The accuracy of the present procedure is demonstrated by application to several pertinent benchmark problems

Computational Considerations for the Simulation of Discontinuous Flows

Abstract: The numerical study of aeroacoustic problems places stringent demands on the choice of a computational algorithm, because it requires the ability to propagate disturbances of small amplitude and short wavelength. The demands are particularly high when shock waves are involved, because the chosen algorithm must also resolve discontinuities in the solution. In a previous work (Casper & Carpenter, 1998) the capabilities and deficiencies of shock-capturing methods for aeroacoustic problems were demonstrated using a high-order essentially nonoscillatory (ENO) numerical method. It was shown that first-order results are obtained when simulating time-dependent flows with discontinuities. The present study reaffirms this conclusion by comparing the ENO results with those obtained using a conventional linear scheme.