Adjoint DSMC Method for Spatially Inhomogeneous Boltzmann Equation with General Boundary Conditions

TL;DR

This paper develops an adjoint DSMC method for the spatially inhomogeneous Boltzmann equation, enabling efficient gradient computations for optimization and sensitivity analysis in rarefied gas dynamics.

Contribution

It introduces a novel adjoint formulation for DSMC that handles various boundary conditions, facilitating advanced analysis and optimization tasks.

Findings

Validated adjoint equations through numerical experiments

Enables gradient-based optimization in rarefied gas simulations

Handles diverse boundary conditions effectively

Abstract

This manuscript derives adjoint equations for the numerical solution of the spatially inhomogeneous Boltzmann equation using Direct Simulation Monte Carlo (DSMC). The formulation accounts for spatial transport and a range of boundary conditions, including periodic boundaries, specular reflection, thermal reflection, and prescribed inflow. Numerical experiments are presented to validate the resulting adjoint system. These adjoint formulations are intended for use in gradient-based optimization, sensitivity analysis, and design problems involving rarefied gas dynamics.