Toward Interoperable Mesh, Geometry and Field Components for PDE Simulation Development

Mesh-based PDE simulation codes are becoming increasingly sophisticated and rely on advanced meshing and discretization tools. Unfortunately, it is still difficult to interchange or interoperate tools developed by different communities to experiment with various technologies or to develop new capabilities. To address these difficulties, we have developed component interfaces designed to support the information flow of mesh-based PDE simulations. We describe this information flow and discuss typical roles and services provided by the geometry, mesh, and field components of the simulation. Based on this delineation for the roles of each component, we give a high-level description of the abstract data model and set of interfaces developed by the Department of Energy's Interoperable Tools for Advanced Petascale Simulation (ITAPS) center. These common interfaces are critical to our interoperability goal, and we give examples of several services based upon these interfaces including mesh adaptation and mesh improvement

Finite volume scheme based on cell-vertex reconstructions for anisotropic diffusion problems with discontinuous coefficients

We propose a new second-order finite volume scheme for non-homogeneous and anisotropic diffusion problems based on cell to vertex reconstructions involving minimization of functionals to provide the coefficients of the cell to vertex mapping. The method handles complex situations such as large preconditioning number diffusion matrices and very distorted meshes. Numerical examples are provided to show the effectiveness of the method

Toward an improved wall treatment for multiple-correction k-exact schemes

Improved wall boundary treatments are investigated for a family of high-order Godunovtype finite volume schemes based on k-exact polynomial reconstructions in each cell of the primitive variables, via a successive corrections procedure. We focus more particularly on the 1-exact and 2-exact schemes which offer a good trade-off between accuracy and computational efficiency. In both cases, the reconstruction stencil needs to be extended to the boundaries. Additionally, information about wall curvature has to be taken into account, which is done by using a surface model based on bicubic Bézier patches for the walls. The performance of the proposed models is presented for two compressible cases, namely the inviscid flow past a Gaussian bump and the viscous axisymmetric Couette flow

A computational study of the effect of unstructured mesh quality on solution efficiency

It is well known that mesh quality affects both efficiency and accuracy of CFD solutions. Meshes with distorted elements make solutions both more difficult to compute and less accurate. We review a recently proposed technique for improving mesh quality as measured by element angle (dihedral angle in three dimensions) using a combination of optimization-based smoothing techniques and local reconnection schemes. Typical results that quantify mesh improvement for a number of application meshes are presented. We then examine effects of mesh quality as measured by the maximum angle in the mesh on the convergence rates of two commonly used CFD solution techniques. Numerical experiments are performed that quantify the cost and benefit of using mesh optimization schemes for incompressible flow over a cylinder and weakly compressible flow over a cylinder

An Unstructured Shock-Fitting Technique For Three-Dimensional Flows With Shock Interactions

The numerical simulation of hypersonic flows past blunt bodies by means of shockcapturing (S-C) solvers is characterized by some critical challenges, including: stagnation point anomalies, spurious numerical oscillations, the carbuncle phenomenon and the reduction of the order of accuracy of the solution in the entire region downstream of a captured shock worsen the solution quality. This paper describes an updated version of the unstructured shock-fitting (S-F) algorithm for three-dimensional flows. In particular, we present a comparison between the results obtained computing hypersonic flows on blunt bodies using both the S-C and S-F techniques on nearly identical tetrahedral meshes, with a special interest on the grid-convergence properties of the two different shock-modeling options

TOWARDS A MODULAR APPROACH FOR UNSTRUCTURED SHOCK-FITTING

We present a modular shock-fitting algorithm for unstructured grids that can be used in conjunction with virtually any vertex-centred shock-capturing solver. The unstructured, shock-fitting algorithm, originally developed for ideal gases, has here been extended to thermochemical nonequilibrium flows and coupled with COOLFluiD, an inhouse shock-capturing CFD solver developed at the Von Karman Institute. Results obtained in the computation of hypersonic flows past circular cylinders are presented for both ideal gas and dissociating Nitrogen in thermochemical nonequilibrium