Bibliographic Details
| Title: |
AN ALGEBRAIC MULTIGRID METHOD FOR OSEEN PROBLEMS. |
| Authors: |
NOTAY, YVAN1 yvan.notay@ulb.be |
| Source: |
SIAM Journal on Scientific Computing. 2025, Vol. 47 Issue 5, pA2506-A2532. 27p. |
| Subjects: |
Algebraic multigrid methods, Multigrid methods (Numerical analysis), Incompressible flow, Numerical analysis, Numerical solutions to equations, Convective flow, Iterative methods (Mathematics) |
| Abstract: |
We consider the numerical solution of discrete Oseen problems. We focus on the recently proposed transform-then-solve approach, which amounts to first applying a specific algebraic transformation to the linear system of equations arising from the discretization and then solving the transformed system with an algebraic multigrid method. Promising results have been previously obtained with a two-grid variant, and here we bring two key improvements to make the approach robust in a multilevel setting. For a model problem with a constant convection field, it is shown, in a local Fourier analysis setting, that the two-grid method is convergent at any level of the hierarchy, with bounds that are independent of both the mesh size and the Reynolds number. Numerical results with a K-cycle multigrid scheme confirm the theoretical expectations for constant coefficient problems. For problems with variable convective flow, the method appears also robust with grid independence convergence, although a mild dependency with respect to the Reynolds number shows up at very low viscosity in driven cavity problems. The method is based on point coarsening and therefore, besides the system matrix, requires knowing, for each discrete unknown, which grid point it is associated with. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
