An Implicit High-Order Spectral Difference Method for the Compressible Navier-Stokes Equations Using Adaptive Polynomial Refinement

by Caleb J. Barnes

Institution: Wright State University
Department: Mechanical Engineering
Degree: MSEgr
Year: 2011
Keywords: Fluid Dynamics; Mechanical Engineering; high-order; spectral difference; CFD; computational fluid dynamics; Euler equations; Euler; gas dynamics; polynomial refinement; adaptive polynomial refinement; artificial dissipation
Record ID: 1925769
Full text PDF: http://rave.ohiolink.edu/etdc/view?acc_num=wright1315591802


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 to approach reference values for each problem. Uniform polynomial refinement was shown to be capable of producing increasingly accurate solutions on a very coarse mesh. Adaptive polynomial refinement was employed to selectively refine the solution near steep gradient structures and results were nearly identical to those produced by uniform polynomial refinement. Future work will focus on improvements to the diffusion term, complete extensions to the full compressible Navier-Stokes equations, and multi-dimension formulations.