Computational Fluid Dynamics for Optimization Using a Summation-by-Parts Discretization and Automatic Differentiation

In multidisciplinary analysis and optimization, computation of aerodynamics is typically handled with second-order finite volume or finite element methods. This paper presents a methodology capable of stable, higher-order discretizations using summation-by-parts operators. Typical finite element and finite difference higher-order operators offer advantages in solution accuracy and computational efficiency but are typically hampered by nonlinear instability. In contrast, summation-by-parts operators can be provably nonlinearly stable. The combination of summation-by-parts operators and an entropy-conservative flux can produce an entropy-stable discretization scheme. This work leverages these operators, an entropy-conservative flux formulation, and automatic differentiation to form a robust solution method. Automatic differentiation is particularly useful in support of the adjoint solver to calculate accurate derivatives with respect to state and design variables.