DNS 1-5 Computational Details: Difference between revisions
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= Computational Details = | = Computational Details = | ||
This section provides details of the computational approach used for the simulation of the present flow problem. Firstly, the main numerical features of the code MIGALE are given. Then, information about the computational grid is provided. Finally, the statistical quantities and their computation are explained. | |||
== Computational approach == | == Computational approach == | ||
The CFD code MIGALE can solve both compressible and incompressible flow problems and implements different flow models ranging from the Euler to the RANS equations. The solver uses the Discontinuous Galerkin (DG) method for the spatial discretization of the governing equations, here the compressible Navier-Stokes equations. The discontinuous nature of the numerical solution requires introducing a special treatment of the inviscid interface flux and of the viscous flux. For the former it is common practice to use suitably defined numerical flux functions, which ensure conservation and account for wave propagation. To this purpose, in the compressible case, the exact Riemann solver of Gottlieb and Groth [1] is mainly used. For the latter, the 2nd-scheme of Bassi and Rebay (BR2) is employed [2]. | The CFD code MIGALE can solve both compressible and incompressible flow problems and implements different flow models ranging from the Euler to the RANS equations. The solver uses the Discontinuous Galerkin (DG) method for the spatial discretization of the governing equations, here the compressible Navier-Stokes equations. The discontinuous nature of the numerical solution requires introducing a special treatment of the inviscid interface flux and of the viscous flux. For the former it is common practice to use suitably defined numerical flux functions, which ensure conservation and account for wave propagation. To this purpose, in the compressible case, the exact Riemann solver of Gottlieb and Groth [1] is mainly used. For the latter, the 2nd-scheme of Bassi and Rebay (BR2) is employed [2]. | ||
Revision as of 16:27, 15 September 2022
Computational Details
This section provides details of the computational approach used for the simulation of the present flow problem. Firstly, the main numerical features of the code MIGALE are given. Then, information about the computational grid is provided. Finally, the statistical quantities and their computation are explained.
Computational approach
The CFD code MIGALE can solve both compressible and incompressible flow problems and implements different flow models ranging from the Euler to the RANS equations. The solver uses the Discontinuous Galerkin (DG) method for the spatial discretization of the governing equations, here the compressible Navier-Stokes equations. The discontinuous nature of the numerical solution requires introducing a special treatment of the inviscid interface flux and of the viscous flux. For the former it is common practice to use suitably defined numerical flux functions, which ensure conservation and account for wave propagation. To this purpose, in the compressible case, the exact Riemann solver of Gottlieb and Groth [1] is mainly used. For the latter, the 2nd-scheme of Bassi and Rebay (BR2) is employed [2]. The devised method uses hierarchical and orthonormal polynomial basis functions defined in the physical (mesh) space and relies for the time integration on, primarily, high-order Rosenbrock linearly-implicit schemes. The Jacobian matrix of the spatial discretization is computed analytically and linear systems are solved using preconditioned GMRES methods from the PETSc library (Portable Extensible Toolkit for Scientific Computations) [4]. For production runs time integration is coupled with time-step adaptation strategies able to improve the robustness and the efficiency in terms of time-to-solution of simulations, [5].
For the present computation the fourth-order DG spatial discretization is combined with the fifth-order eight stages Rosenbrock-type scheme of Di Marzo [6].
References
[1] J.J.Gottlieb, C.P.T.Groth, “Assessment of Riemann solvers for unsteady one-dimensional inviscid flows of perfect gases”, J. Comput. Phys. 78, 1988
[2] F. Bassi, S.Rebay, G.Mariotti, S.Pedinotti, M.Savini, “A high-order accurate discontinuous finite element method for inviscid and viscous turbomachinery flows”, in: R. Decuypere, G. Dibelius (Eds.), Proceedings of the 2nd European Conference on Turbomachinery Fluid Dynamics and Thermodynamics, Technologisch Instituut, Antwerpen, Belgium, 1997
[3] Bassi, F., Botti, L., Colombo, A., Ghidoni, A., Massa, F., “Linearly implicit Rosenbrock-type Runge-Kutta schemes applied to the Discontinuous Galerkin solution of compressible and incompressible unsteady flows”, Computers and Fluids, 2015
[4] PETSc Web page
[5] G. Noventa, F. Massa, S. Rebay, F. Bassi, A. Ghidoni, “Robustness and efficiency of an implicit time-adaptive discontinuous Galerkin solver for unsteady flows”, Computers & Fluids, 2020
[6] Di Marzo, G., “RODAS5(4) - Méthodes de Rosenbrock d'ordre 5(4) adaptées aux problèmes différentiels-algébriques", MSc Mathematics Thesis, Faculty of Science, University of Geneva, 1993
Spatial and temporal resolution, grids
Discuss the resolution of the simulation. If possible, relate it to the spectral accuracy. Indicate the dependence of the formal accuracy of the code to the quality of the mesh. Discuss the procedure for the a priori estimation of the grid resolution. Finally, provide the grids used for the study.
Computation of statistical quantities
Describe how the averages and correlations are obtained from the instantaneous results and how
terms in the budget equations are computed, in particular if there are differences to the proposed
approach in Introduction.
Contributed by: Francesco Bassi, Alessandro Colombo, Francesco Carlo Massa — Università degli studi di Bergamo (UniBG)
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