Extension of a Post Processing Technique for the Discontinuous Galerkin Method for Hyperbolic Equations with Application to an Aeroacoustic Problem

One-sided Post-processing for the Discontinuous Galerkin Method Using ENO Type Stencil Choosing and the Local Edge Detection Method

“…In addition, numerical evidence strongly indicates that the method also improves the convergence for non-linear problems as well. The applications of the post-processor were extended in [19] to include multi-domains with different mesh sizes as well as variable and discontinuous coefficient equations. The extension of this technique to one-sided post-processing appears in [20].…”

“…The extension of this technique to one-sided post-processing appears in [20]. Detailed discussion of the post-processor, including implementation, can be found in [7,8,19,20].…”

“…where ψ (k+1) (x) is obtained by convolving the characteristic function over the interval (− 1 2 , 1 2 ) with itself k times and c 2(k+1),k+1 γ ∈ R. The calculation of c 2(k+1),k+1 γ as well as the construction and implementation of (2.3) is described in [3,19,20,22,23].…”

“…We note that since we are using an uniform mesh, the kernel (2.4) has a particularly simple form as in [7,8,19,20]. Furthermore, the postprocessor as well as the B-spline coefficients are symmetric.…”

“…The solution is computed to time T f = 1.0, which is before the shocks cross. The error in the numerical solution and in the first derivative of the solution is calculated to include the stationary shocks at x = ±1, but to exclude a radius of 0.1 around the moving shocks as in [19,20].…”