## A multigrid method for solving the Navier-Stokes/Boussinesq equations.(English)Zbl 1159.76355

Summary: The present work investigates the efficiency and the accuracy of a multigrid (MG) technique for solving the Navier-Stokes/Boussinesq equations. In order to improve convergence, an accelerated full multigrid (AFMG) method with the iterative red and black successive over-relaxation smoother (RBSOR) is utilized. The AFMG method consists in introducing an accelerated parameter $$\Gamma >0$$ in the standard full multigrid procedure (FMG). A well-known benchmark problem is used to demonstrate the effectiveness and the accuracy of the method. Solutions are compared with those of the literature and show excellent agreement. Results for Prandtl numbers $$Pr=12.5, 6.8, 0.71$$ and 0.025 are also presented in this paper. It is observed that the mean heat transfer rate is minimum for $$Pr=0.71$$ and maximum for $$Pr=0.025$$.

### MSC:

 76M12 Finite volume methods applied to problems in fluid mechanics 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 76R10 Free convection

### Keywords:

finite-volume; multigrid; natural convection; projection method
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### References:

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