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An Implicit High-Order Spectral Difference Method For The Compressible Navier-Stokes Equations Using Adaptive Polynomial Refinement, Caleb J. Barnes

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A high/variable-order numerical simulation procedure for gas dynamics problems was developed to model steep grading physical phenomena. Higher order resolution was achieved using an orthogonal polynomial Gauss-Lobatto grid, adaptive polynomial refinement and artificial diffusion activated by a pressure switch. The method is designed to be computationally stable, accurate, and capable of resolving discontinuities and steep gradients without the use of one-sided reconstructions or reducing to low-order. Solutions to several benchmark gas-dynamics problems were produced including a shock-tube and a shock-entropy wave interaction. The scheme's 1st-order solution was validated in comparison to a 1st-order Roe scheme solution. Higher-order solutions were shown …