A projection method based on Gaussian quadratures with application to compressible Navier-Stokes equations
A projection method based on Gauss-Legendre quadratures for solving hyperbolic and parabolic partial differential equations is proposed. It is comparable to spectral methods in accuracy and convergence, and is more convenient to implement for non-linear problems. Results obtained with a wave equation and Burgers equation modeling a flow with sharp gradients show the high resolution achieved for a given number of nodes by using this method. Time-split implicit techniques are used for approximating the compressible Navier-Stokes equations.
KeywordsProjection Method Burger Equation Parabolic Partial Differential Equation Gaussian Node Implicit Trapezoidal Rule
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