Unified Error Transport Equation Solver for Solution Verification on Unstructured Grids

Abstract

Error quantification is a subject of importance for any Computational Fluid Dynamics (CFD) simulation. Only when errors due to the computational mesh, iterative convergence, and code usage are bounded can errors due to physical modeling be properly examined. The current work extends an existing error prediction method, based on the solution of Error Transport Equations (ETE), to a unified framework suitable for use with simulations conducted using cell-centered or node-centered finite volume unstructured Navier-Stokes solvers. Support for the CGNS standard has been implemented to permit use of the method by a broad spectrum of potential flow solvers. Applications are presented demonstrating the solver's utility as a practical and effective solution verification tool for a variety of turbulence models and CFD codes. 2The Error Transport Equation (ETE) Solver presented and developed in this work is integrated in the CRISP CFD ® code, a parallel solution adaptation and error quantification suite for 3D mixed element unstructured grids. While previous work was focused on the development of the error transport model within a node-centered discretization, the current effort emphasizes developing a unified framework for error prediction suitable for use with a number of current state-of-the-art flow solvers. In particular, the discretization of the ETE should match that of the flow solver as closely as possible to provide a truly accurate representation of the error for a given grid. On a tetrahedral mesh, for example, the number of cells is 5-6 times the number of vertices, and analyzing a cell-centered CFD solution using a node-centered discretization for the ETE is inappropriate since a coarser grid is being employed. Modern unstructured grid solvers employ a variety of turbulence models. The ETE solver is shown to be applicable to several popular RANS models such as Spalart-Allmaras, k- and k-. Case studies are presented using simulations from the node-centered codes CRUNCH CFD ® [18] and FUN3D [19] along with the cell-centered codes AVUS [20] and USM3D [21]. Support for the CGNS standard [22] has also been implemented and permits use of the suite by a broader spectrum of potential Navier-Stokes solvers. With these new developments, the ETE Solver in CRISP CFD ® represents a useful solution verification capability for general application.