Application of a domain decomposition method in the direct numerical simulation of thermal convection with boiling
(2024) 1st European Fluid Dynamics Conference — Location: Aachen, Germany (16.September.2024)
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- Abstract
- The method of Domain Decomposition (DD) has emerged as an important branch of parallel computing due to its potential to reduce the computational cost of solving partial differential equations. Over the past decades this method has been successfully applied to resolve wall-bounded turbulent flows in both the Reynolds-Averaged-Navier-Stokes (RANS) and Large-Eddy Simulation (LES) frameworks. On the other hand, this method has been applied to a much less extent in Direct Numerical Simulations (DNS). In this talk, we elaborate on our development of a non-overlapping domain decomposition method for application in DNS of thermal convection with the aim of exploiting the computational advantages that DD can offer. In the first part of the talk, we present the theoretical convergence analysis of this DD method when applied to Poisson equation 1, which plays a crucial role in resolving the pressure field in fluid flow simulations. It is important to note that the convergence rate of this DD method depends only on the symbols of the Steklov- Poincar´e operators applied to the equation. Therefore, the convergence result makes general sense for a whole class of problems rather than just an individual one. In particular, for the flows of interest, we employ the low-Mach-number solver 2 which employs a projection method for resolving the pressure field. However, the projection step results in a Poisson equation for the pressure that must be solved at each time step. The solution of this Poisson equation constitutes the most expensive and delicate part of the entire solver. This is where the proposed DD method can be applied to increase the efficiency of the simulation: to solve the Poisson equation in several subdomains in parallel with more efficient data exchange on the interfaces. In the second part of the talk we elaborate on the numerical implementation of the proposed DD method. We also investigate the computational savings of this method by solving numerically the Poisson equation and comparing the numerical results with the theoretically predicted convergence rates. Additionally we show, both theoretically and numerically, that the computational savings of the proposed DD method are more significant than those of conventional DD schemes for the problems of interest. Finally, we discuss the applicability of the proposed DD method in solving other BVPs than the Poisson equation in the broader context of thermal and fluid flow simulation. *
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