Title: A Continuum Runge–Kutta Framework for Coupled Eulerian–Semi-Lagrangian Kinetic Models
Abstract: Semi-Lagrangian and Eulerian methods are natural numerical frameworks for kinetic and fluid transport, respectively, but coupling them within a unified high-order temporal discretization remains challenging, particularly in the presence of stiff nonlinear collisions. We address this challenge by recasting the kinetic equation as a continuum-indexed system of ordinary differential equations for the characteristic map and Lagrangian kinetic density and applying a single nonlinearly partitioned Runge--Kutta (NPRK) method to the resulting system together with the Eulerian fluid state. Kinetic quadrature closes the continuum stage equations, and, for a sequential subclass of NPRK methods, the kinetic stages reduce to independent trajectory-local solves followed by a moment reduction. This construction yields efficient higher-order time integrators and same-stage embedded error estimators for adaptive stepping. We realize the framework for a binary neutral-gas BGK model. Numerical experiments verify the designed temporal, spatial, and velocity-quadrature convergence, validate the embedded error estimators and adaptive time stepping, recover stiff relaxation limits, and demonstrate finite-collisionality kinetic shock structure.
Bio: I am a second-year Director’s Postdoctoral Fellow in T-5 at Los Alamos National Laboratory. My research includes PDE-based conservative regularizations of hydrodynamic shocks, radiative-transfer models for high-frequency elastic waves, semi-analytical reconstruction of radiative plasma shock profiles, and time-integration methods coupling Eulerian fluid models with semi-Lagrangian kinetic models. A common thread across these projects is my interest in structure-preserving numerical methods for fluid, plasma, and transport problems characterized by extreme asymptotic scale separation.