A pressure-correction ensemble scheme for computing evolutionary Boussinesq equations. (English) Zbl 1466.65137
Summary: We study a pressure-correction ensemble scheme for fast calculation of thermal flow ensembles. The proposed scheme (1) decouples the Boussinesq system into two smaller subphysics problems; (2) decouples the nonlinearity from the incompressibility condition in the Navier-Stokes equations and linearizes the momentum equation so that it reduces to a system of scalar equations; (3) results in linear systems with the same coefficient matrix for all realizations. This reduces the size of linear systems to be solved at each time step and allows efficient direct/iterative linear solvers for fast computation. We prove the scheme is long time stable and first order in time convergent under a time step condition. Numerical tests are provided to confirm the theoretical results and demonstrate the efficiency of the scheme.
MSC:
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
Keywords:
Boussinesq equations; ensemble method; pressure-correction method; uncertainty quantificationSoftware:
FreeFem++References:
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