An implicit Lower-Upper Symmetric Gauss-Seidel (LU-SGS) solver has been implemented as a multigrid smoother combined with a line-implicit method as an acceleration technique for Reynolds-Averaged Navier-Stokes (RANS) simulation on stretched meshes. The Computational Fluid Dynamics code concerned is Edge, an edge-based finite volume Navier-Stokes flow solver for structured and unstructured grids. The paper focuses on the investigation of the parameters related to our novel line-implicit LU-SGS solver for convergence acceleration on 3D RANS meshes. The LU-SGS parameters are defined as the Courant-Friedrichs-Lewy number, the Left Hand Side dissipation, and the convergence of iterative solution of the linear problem arising from the linearisation of the implicit scheme. The influence of these parameters on the overall convergence is presented and default values are defined for maximum convergence acceleration. The optimized settings are applied to 3D RANS computations for comparison with explicit and line-implicit Runge-Kutta smoothing. For most of the cases, a computing time acceleration of the order of 2 is found depending on the mesh type, namely the boundary layer and the magnitude of residual reduction.
Postprocessing and storage of large data sets represent one of the main computational bottlenecks in computational fluid dynamics. We assume that the accuracy necessary for computation is higher than needed for postprocessing. Therefore, in the current work we assess thresholds for data reduction as required by the most common data analysis tools used in the study of fluid flow phenomena, specifically wall-bounded turbulence. These thresholds are imposed a priori by the user in L 2 -norm, and we assess a set of parameters to identify the minimum accuracy requirements. The method considered in the present work is the discrete Legendre transform (DLT), which we evaluate in the computation of turbulence statistics, spectral analysis and resilience for cases highly-sensitive to the initial conditions. Maximum acceptable compression ratios of the original data have been found to be around 97%, depending on the application purpose. The new method outperforms downsampling, as well as the previously explored data truncation method based on discrete Chebyshev transform (DCT).
The implicit Lower-Upper Symmetric Gauss-Seidel solver is combined with the line-implicit technique to improve convergence on the very anisotropic grids necessary for resolving the boundary layers. The computational fluid dynamics code used is Edge, a Navier-Stokes flow solver for unstructured grids based on a dual grid and edge-based formulation. Multigrid acceleration is applied with the intention to accelerate the convergence to steady state. Lower-Upper Symmetric Gauss-Seidel works in parallel and gives better linear scaling with respect to the number of processors, than the explicit scheme. The ordering techniques investigated have shown that node numbering does influence the convergence and that the orderings from Delaunay and advancing front generation were among the best tested. 2D ReynoldsAveraged Navier-Stokes computations have clearly shown the strong efficiency of our novel approach line-implicit Lower-Upper Symmetric Gauss-Seidel which is four times faster than implicit Lower-Upper Symmetric Gauss-Seidel and line-implicit Runge-Kutta. Implicit Lower-Upper Symmetric Gauss-Seidel for Euler and line-implicit Lower-Upper Symmetric Gauss-Seidel for Reynolds-Averaged Navier-Stokes are at least twice faster than explicit and line-implicit Runge-Kutta, respectively, for 2D and 3D cases. For 3D Reynolds-Averaged Navier-Stokes, multigrid did not accelerate the convergence and therefore may not be needed.
An implicit Lower-Upper Symmetric Gauss-Seidel (LU-SGS) solver has been implemented as a multigrid smoother combined with a line-implicit method as an acceleration technique for Reynolds-Averaged Navier-Stokes (RANS) simulation on stretched meshes. The Computational Fluid Dynamics code concerned is Edge, an edge-based finite volume Navier-Stokes flow solver for structured and unstructured grids. The paper focuses on the investigation of the parameters related to our novel line-implicit LU-SGS solver for convergence acceleration on 3D RANS meshes. The LU-SGS parameters are defined as the Courant-Friedrichs-Lewy number, the Left Hand Side dissipation, and the convergence of iterative solution of the linear problem arising from the linearisation of the implicit scheme. The influence of these parameters on the overall convergence is presented and default values are defined for maximum convergence acceleration. The optimized settings are applied to 3D RANS computations for comparison with explicit and line-implicit Runge-Kutta smoothing. For most of the cases, a computing time acceleration of the order of 2 is found depending on the mesh type, namely the boundary layer and the magnitude of residual reduction.
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