A multigrid factorization technique for the flux-split Euler equations
The Euler equations formulated in characteristic components are solved by a time-like finite-difference method based on implicit multilevel grid sequencing. The conservative equations are made quasi-linear in metric coefficients in order to use upwind difference approximation of second order for the entire domain. Inside the computation region, the appropriate difference formula is automatically selected in accordance with the sign of the characteristics. When the flux components are originated outside the region, they are discarded and boundary conditions are imposed. Because the propagation path of signals is properly accounted for, higher accuracies of the solution and greater robustness of the numerical procedure are obtained. The implicit factorization procedure, which relies on the solution of four scalar matrices rather than of one block pentadiagonal matrix to save computation time, has removed severe restrictions on the time-step increments. Further more, the convergence rate is accelerated by a multigrid algorithm that switches the implicit procedure from fine to successively coarser grid levels. Newton's method is used to linearize the difference equations at the beginning of each step, then the correction vector is determined from the factorization technique applied to each grid level. Two-dimensional examples of a supersonic inlet flow and a transonic airfoil flow are considered in this study.
KeywordsGrid Level Multigrid Algorithm Correction Vector Multigrid Technique Implicit Procedure
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