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Center for Nonlinear Studies |
Code Verification is the act of ensuring that a PDE code is solving its governing equations correctly, i.e., to the formal order-of-accuracy of its numerical algorithms. An accurate solution to the PDE code's governing equations is needed, then, to evaluate the codes error. Exact solutions of sufficient complexity are generally not available for codes designed to solve realistic problems. A popular alternative to using exact solutions is the Method of Manufactured Solutions (MMS), which can be used to generate solutions to the PDE code's governing equations at the cost of requiring the addition of source terms to the PDE code. While MMS has been used successfully in many situations, deriving and implementing the source terms may be cumbersome. External Verification Analysis (EVA) attempts to overcome this difficulty for unsteady problems. Similar to MMS, an analytical spatial distribution of the initial flow is specified. With EVA, the solution at a later time level is found using a temporal Taylor series centered at the initial time. The coefficients of the series are calculated through repeated differentiation of the governing equations with the analytic spatial distribution of the initial solution. The solution at the later time level is then used with grid or timestep studies to verify the PDE code. The EVA approach does not require any modification to be made to the PDE code, allowing the user to treat it as a ``black box'' during the verification process. In this work, the details of the EVA method will be presented, and results from its application to BASS, NASA Glenn's high-order Computational Aeroacoustics code, will be shown.
Host: Mikhail Shashkov, XCP-4 Methods and Algorithms, 667-4400