High Performance Computing with a Conservative Spectral Boltzmann Solver
This work provides an efficient, high-order numerical method for the Boltzmann equation, enabling simulations of non-equilibrium gas dynamics that are inaccessible to traditional hydrodynamic models.
The authors extend a conservative spectral Boltzmann solver to second-order accuracy in space and time and demonstrate its scalability on HPC resources, enabling simulation of a boundary-layer shock problem beyond classical hydrodynamics.
We present new results building on the conservative deterministic spectral method for the space inhomogeneous Boltzmann equation developed by Gamba and Tharkabhushaman. This approach is a two-step process that acts on the weak form of the Boltzmann equation, and uses the machinery of the Fourier transform to reformulate the collisional integral into a weighted convolution in Fourier space. A constrained optimization problem is solved to preserve the mass, momentum, and energy of the resulting distribution. We extend this method to second order accuracy in space and time, and explore how to leverage the structure of the collisional formulation for high performance computing environments. The locality in space of the collisional term provides a straightforward memory decomposition, and we perform some initial scaling tests on high performance computing resources. We also use the improved computational power of this method to investigate a boundary-layer generated shock problem that cannot be described by classical hydrodynamics.