Sparse Preconditioners for Hypersonic Flows with Second-Order Transport: Analytic Jacobians Versus Automatic Differentiation

Efficient simulations of hypersonic flows are challenging due to the stiffness of the mathematical system formed by time-implicit solvers. Iterative methods alleviate the mesh-size cost scaling of direct methods but require effective preconditioning, particularly for highly multiresolution meshes. We additionally consider second-order molecular transport terms, necessary for transition-continuum hypersonic flows, that impart stability requirements beyond those of first-order transport terms. Automatic differentiation (AD) is the state-of-the-art method to obtain sparse, discrete-exact Jacobian preconditioners and avoids the difficulty and potential error of analytic derivations. However, AD typically incurs higher computational cost than analytically derived Jacobian preconditioners. We derive analytic viscous and inviscid flux Jacobians for unstructured finite-volume discretizations with contributions of second-order constitutive terms. For transition-continuum flow of argon over a flat plate at M_∞= 3.27, we compare the convergence and computational cost of Krylov-subspace solvers using the analytically derived block-sparse Jacobians and AD-computed block-sparse Jacobians. We additionally investigate the scaling of each method's memory requirements and computational cost for problems of varying mesh density and project the performance of each for vehicle-scale meshes.