A massively parallel algorithm for the three-dimensional navier-stokes-boussinesq simulations of the atmospheric phenomena

Abstract

We present a massively parallel solver using the direction splitting technique and stabilized time-integration schemes for the solution of the three-dimensional non-stationary Navier-Stokes-Boussinesq equations. The model can be used for modeling atmospheric phenomena. The time integration scheme utilized enables for efficient direction splitting algorithm with finite difference solver. We show how to incorporate the terrain geometry into the simulation and how to perform the domain decomposition. The computational cost is linear O(N) over each sub-domain, and near to O(N/c) in parallel over 1024 processors, where N is the number of unknowns and c is the number of cores. This is even if we run the parallel simulator over complex terrain geometry. We analyze the parallel scalability experimentally up to 1024 processors over a PROMETHEUS Linux cluster with multi-core processors. The weak scalability of the code shows that increasing the number of sub-domains and processors from 4 to 1024, where each processor processes the subdomain of 49× 49× 99 internal points (50× 50× 100 box), results in the increase of the total computational time from 120 s to 178 s for a single time step. Thus, we can perform a single time step with over 1,128,000,000 unknowns within 3 min. The number of unknowns results from the fact that we have three components of the velocity vector field, one component of the pressure, and one component of the temperature scalar field over 256,000,000 mesh points. The computation of the one time step takes 3 min on a Linux cluster. The direction splitting solver is not an iterative solver; it solves the system accurately since it is equivalent to Gaussian elimination. Our code is interfaced with the mesh generator reading the NASA database and providing the Earth terrain map. The goal of the project is to provide a reliable tool for parallel, fully three-dimensional computations of the atmospheric phenomena.