Adjoint DSMC Method for Spatially Inhomogeneous Boltzmann Equation with General Boundary Conditions
This work addresses the need for efficient gradient computation in optimization problems for rarefied gas dynamics, though it is incremental as it extends existing adjoint methods to more complex boundary conditions.
The authors derived adjoint equations for the Direct Simulation Monte Carlo (DSMC) method to solve the spatially inhomogeneous Boltzmann equation with various boundary conditions, and validated them through numerical experiments for applications in gradient-based optimization and sensitivity analysis in rarefied gas dynamics.
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.