Numerical dispersion analysis of the convected Helmholtz equation
Provides theoretical and numerical insights into dispersion errors for finite element solutions of the convected Helmholtz equation, relevant for computational acoustics.
The paper analyzes numerical dispersion in solving the convected Helmholtz equation using conforming and nonconforming quadrilateral finite elements, deriving dispersion relations and verifying them with numerical experiments.
We present the numerical dispersion effects in solving the convected Helmholtz equation by the conforming and nonconforming quadrilateral finite elements. Particularly, we evaluate the dispersion relations for the numerical schemes. The dispersive behaviors are analyzed by focusing on the Mach number and the angular frequency. Numerical experiments are conducted to verify the relations between the numerical dispersions and the computational errors.