Simulation and Adjoint-Based Design for Variable Density Incompressible Flows with Heat Transfer

Abstract

This paper details the development and implementation of a density-based solution approach for simulation and design in variable density incompressible flows with heat transfer. In the low-Mach approximation of the Navier–Stokes equations, density can vary as a function of transported scalars, and in this case, density varies with temperature from a coupled energy equation. These governing equations are spatially discretized using a finite volume method on unstructured grids and solved in a coupled manner with a generalized artificial compressibility method. Complete details of the numerical implementation are provided, and it has been algorithmically differentiated to construct a discrete adjoint for efficient sensitivity analysis. Results demonstrating the primal solver on a set of standard verification and validation cases and adjoint-based shape optimization are presented.