Adaptive, scalable relativistic Fokker-Planck-Boltzmann solver based on PETSc-p4est

Johann Rudi (ANL), Max Heldman (ANL and Boston), Emil Constantinescu (ANL), Qi Tang (LANL) and Xianzhu Tang (LANL)

LA-UR-22-22439. Approved for public release; distribution is unlimited.

Overview

We consider a 0D2V relativistic Fokker-Planck equation for runaway electrons \begin{align} \frac{\partial f}{\partial t} - eE_\parallel \left(\xi\frac{\partial f}{\partial p} + \frac{1-\xi^2}{p} \frac{\partial f}{\partial\xi} \right) = C_{\rm col}(f) + C_{\rm rad}(f) + C_{\rm Chiu}(f), \end{align} where $C_{\rm col}(f)$ is a Columbo collision operator, $C_{\rm rad}(f)$ a radiation damping operator, and $C_{\rm Chiu}(f)$ is a secondary knock on collision source. We develop a scalable fully implicit solver with dynamic adaptivity. We developed a new data management framework in PETSc based on the p4est library that enables simulations with dynamic adaptive mesh refinement (AMR), and implemented a new runaway electron solver that interfaces to the PETSc framework.

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Result

The simulation demonstrates the critical need for AMR¹, in which 7 levels of refinement are used (corresponding to a 128 factor of resolution increase) to resolve both low-energy Maxwellian bulk and high-energy runaway tail. The dynamic AMR successfully captures the interaction between two structures and resolves a forming vortex structure. A delta-function-like Chiu source and practical collision parameters extracted from ITER are also deployed.

MPI Ranks are presented to demonstrate dynamic load balancing. Here 64 CPUs are used in this AMR run. Unlike the MFEM MHD work which uses a Hilbert curve, here a "zig-zag" space filling curve is used which results into discontinuity in domain decompositions.