Eventos Anais de eventos
ENCIT 2016
16th Brazilian Congress of Thermal Sciences and Engineering
EVALUATION OF IMPLICIT TIME MARCHING SCHEMES FOR HIGH-ORDER SPECTRAL DIFFERENCE METHODS
Submission Author:
Eduardo Jourdan , SP
Co-Authors:
Fábio Malacco Moreira, Carlos Breviglieri, André Ribeiro de Barros Aguiar, João Luiz F. Azevedo
Presenter: Eduardo Jourdan
doi://10.26678/ABCM.ENCIT2016.CIT2016-0154
Abstract
There is an active research CFD community working on high-order methods for unstructured meshes. In order to compete with industrial-level CFD solvers, there are yet some difficulties to be overcome in high-order simulations for practical aerospace applications. Improving computational efficiency and robustness is one aspect of great importance, and a reasonable number of implicit time schemes have been already developed. In steady problems, the use of implicit time integration schemes makes possible to advance the solution with larger time steps and, therefore, achieve convergence in less CPU time. On the other hand, high order space discretizations come together with very large Jacobian matrices, consuming a significant amount of memory and time. With that observation in mind, the present work presents an evaluation of different time marching schemes along with the Spectral Difference (SD) method for the resolution of two-dimensional inviscid compressible flows. The study cases considered were the inviscid Ringleb flow, and subsonic and supersonic flow around a NACA 0012 airfoil. For each of these cases, three different approaches for time marching schemes were used: an explicit 3rd-order 4-stage Runge Kutta scheme, a GMRES (Generalized Minimal Residual) method and a LU-SGS (Lower-Upper Symmetric Gauss Seidel) scheme. For each one of these methods, performance was evaluated regarding convergence rate, CPU time and memory usage. The GMRES method is an iterative solver for sparse linear system that makes use of the full Jacobian matrices and actually solves for all degrees of freedom of the entire mesh in the same linear system. On the other hand, the LU-SGS approach is another type of iterative solver that only needs part of the Jacobian matrices and considers separately the linear system generated for each cell in the domain. The analytical expressions for the Jacobian matrices were quite laborious to be formulated and, therefore, a numerical calculation approach was used. The GMRES method and the LU decomposition needed inside LU-SGS were implemented with an external package called PETCs, a well-known parallel linear system solver library. For the GMRES scheme to be successful and robust enough between different study cases, a preconditioner was applied. The Incomplete Lower-Upper decomposition (ILU) was first considered and utilized in this study and ongoing tests are been performed with other different preconditioners.
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