SUMMARYAdjoint-based and feature-based grid adaptive strategies are compared for their robustness and effectiveness in improving the accuracy of functional outputs such as lift and drag coefficients. The output-based adjoint approach strives to improve the adjoint error estimates that relate the local residual errors to the global error in an output function via adjoint variables as weight functions. A conservative adaptive indicator that takes into account the residual errors in both the primal (flow) and dual (adjoint) solutions is implemented for the adjoint approach. The physics-based feature approach strives to identify and resolve significant features of the flow to improve functional accuracy. Adaptive indicators that represent expansions and compressions in the flow direction and gradients normal to the flow direction are implemented for the feature approach. The adaptive approaches are compared for functional outputs of three-dimensional arbitrary Mach number flow simulations on mixed-element unstructured meshes. Grid adaptation is performed with h-refinement and results are presented for inviscid, laminar and turbulent flows.
SUMMARYParallel discrete direct and adjoint sensitivity analysis capabilities are developed for arbitrary Mach flows on mixed-element unstructured grids. The discrete direct and adjoint methods need a consistent and complete linearization of the flow-solver to obtain accurate derivatives. The discontinuous nature of the commonly used unstructured flux-limiters, like Barth-Jespersen and Venkatakrishnan, make them unsuitable for sensitivity analysis. A modification is proposed to make these limiters piecewise continuous and numerically differentiable, without compromising the monotonicity conditions. An improved version of Symmetric Gauss-Seidel that significantly reduces the computational cost is implemented. A distributed-memory message passing model is employed for the parallelization of sensitivity analysis solver. These algorithms are implemented within a three-dimensional unstructured grid framework and results are presented for inviscid, laminar and turbulent flows.
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