A publication of the Advanced Simulation & Computing Division, NA-121.2, NNSA Defense Programs
June 2009
NA-ASC-500-09—Issue 11
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Enhanced Verification Test Suite Completed for Physics Simulation Codes
A tri-lab team has completed a multiyear effort to identify and develop verification test problems to assess the numerical performance of models and algorithms implemented in ASC codes. The purpose of the verification analysis is to demonstrate whether the numerical results of the discretization algorithms in physics and engineering simulation codes provide correct solutions of the corresponding continuum equations.
Led by James Kamm, at Los Alamos National Laboratory (LANL), David Cotrell, at Lawrence Livermore National Laboratory (LLNL), and Greg Weirs, at Sandia National Laboratories (SNL), the collaboration culminated in a published report that supplements a 1999 report that documented seven problems. The May 2009 report¹ adds nineteen problems to the original list of seven problems while providing better coverage of hydrodynamics equations, transport processes, and strength of materials. While these test problems are not intended to comprise an exhaustive list, they provide a starting point for a common comparison of simulation codes at the laboratories and elsewhere. The rigor with which simulation codes of the NNSA weapons laboratories are assessed is greatly improved by analyzing code verification test problems. Only the comparison between the exact solutions of these test problems and numerical approximations calculated by a code provides a quantitative evaluation of code quality, credibility, and usefulness.
Figure 1 is a “view-graph” norm comparison between an exact solution and four approximations calculated by an ASC hydrodynamics code at LANL. The four solutions are obtained using coarse- to- fine levels of mesh discretization. To go beyond a qualitative “view-graph norm,” errors between the exact and numerical solutions must be calculated, which the second figure shows. Plotting the solution error as a function of mesh resolution indicates the behavior of truncation error. Assessing the behavior of truncation error is important for two reasons. First, it verifies the correctness of an algorithm or model implementation because, if implemented correctly, then the theoretical order of convergence of the numerical method should be recovered. Second, it provides important insight into which discretization settings are appropriate to simulate a particular phenomenon that may be of interest to code users.
Figure 1. Comparison of exact and discrete solutions from a mesh refinement study.
Figure 2. Analysis of solution error as a function of mesh resolution in the calculation.
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