An embedded boundary method for viscous, conducting compressible flow

The evolution of an inertial fusion energy (IFE) chamber involves a repetition of short, intense depositions of energy (from target ignition) into a reaction chamber, followed by the turbulent relaxation of that energy through shock waves and thermal conduction to the vessel walls. We present an algorithm for 2D simulations of the fluid inside an IFE chamber between fueling repetitions. Our finite-volume discretization for the Navier–Stokes equations incorporates a Cartesian grid treatment for irregularly-shaped domain boundaries. The discrete conservative update is based on a time-explicit Godunov method for advection, and a two-stage Runge–Kutta update for diffusion accommodating state-dependent transport properties. Conservation is enforced on cut cells along the embedded boundary interface using a local redistribution scheme so that the explicit time step for the combined approach is governed by the mesh spacing in the uniform grid. The test problems demonstrate second-order convergence of the algorithm on smooth solution profiles, and the robust treatment of discontinuous initial data in an IFE-relevant vessel geometry.