An Example of Code Verification in the Simulation of Wave Propagation

Abstract

Thanks to advances in modeling and hardware the range of applications available to CFD modeling is continuously increasing. As CFD has moved from demonstration of capability to production of engineering results of practical value, there is an increased awareness in the field that Verification and Validation are systematically required. Verification deals with the numerical accuracy of a given set of results. Its object is the assessment of the numerical uncertainty due to discretization and iterative errors of a numerical solution (Solution Verification) performed with a Code that has been previously checked to be free of errors (Code Verification). Both activities are required to ensure that errors are controlled and that quality of the results is maintained. Complementarily, Validation addresses the modeling error, i.e. the comparison of the mathematical model with the (physical) reality. Therefore, it requires comparison with experimental data. Validating CFD results is only meaningful when preceded by carefully verified calculations (Solution Verification) with verified codes (Code Verification). The topic of Verification and Validation is developing and standardized procedures are still under discussion. Nevertheless, there are techniques available to perform careful Code and Solution Verification for flows with engineering relevance. This paper presents a Code Verification exercise for the simulation of wave propagation with a VOF code. Systematically refined grids and time steps are applied in the calculation of waves with a known analytical solution to assess the convergence properties of the numerical solution. The aim of the exercise is to demonstrate the advantages of such exercises for the knowledge of the numerical properties of a code that is applied in complex flows. The study is not a pure Code Verification exercise. Modeling errors introduced by approximate outlet boundary conditions (allowing wave reflections) are also quantified for a linear and a high-order wave. However, these are still based on (numerical) error evaluations for known analytical solutions and so they can still be classified as Code Verification.