Special Session 100: 

Fast Kinetic Scheme : efficient MPI parallelization strategy for 3D Boltzmann equation

Jacek Narski
Toulouse University
France
Co-Author(s):    
Abstract:
In the kinetic theory of gases, the state of the system is described by the distribution function defined in seven independent dimensions: the physical space, the velocity space and time. Moreover, the interaction between particles requires multiple integrals over velocity space to be evaluated at every space point and for every time step of the numerical method. This makes the kinetic theory very challenging from numerical view point. In this talk, we present an efficient parallelization strategy to solve full Boltzmann equation in 6D by means of a deterministic semi-Lagrangian scheme and a fast spectral method for computing the collision integral in $O(N\log N)$. The spatial degrees of freedom are distributed over computational nodes, keeping on every mode a complete velocity space so the integrals involved in the Boltzmann collision operator can be solved with no additional communication between nodes. Moreover, the collision operator is GPU/OpenMP parallelized on each node. As a result, the strong scaling is close to ideal in the tested range (up to 1024 computational nodes). Numerical examples include fine grid $3D\times 3D$ numerical simulations of the Boltzmann equation.