Dispersion-relation-preserving finite difference schemes for computational acoustics
Journal of Computational Physics
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Spectral methods for hyperbolic problems
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
Computational aspects of the ultra-weak variational formulation
Journal of Computational Physics
The Ultra-Weak Variational Formulation for Elastic Wave Problems
SIAM Journal on Scientific Computing
A new category of Hermitian upwind schemes for computational acoustics
Journal of Computational Physics
Journal of Computational Physics
Discontinuous Galerkin method based on non-polynomial approximation spaces
Journal of Computational Physics
Solving Maxwell's equations using the ultra weak variational formulation
Journal of Computational Physics
Plane Wave Discontinuous Galerkin Methods for the 2D Helmholtz Equation: Analysis of the $p$-Version
SIAM Journal on Numerical Analysis
The ultra weak variational formulation of thin clamped plate problems
Journal of Computational Physics
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A general framework for discontinuous Galerkin methods in the frequency domain with numerical flux is presented. The main feature of the method is the use of plane waves instead of polynomials to approximate the solution in each element. The method is formulated for a general system of linear hyperbolic equations and is applied to problems of aeroacoustic propagation by solving the two-dimensional linearized Euler equations. It is found that the method requires only a small number of elements per wavelength to obtain accurate solutions and that it is more efficient than high-order DRP schemes. In addition, the conditioning of the method is found to be high but not critical in practice. It is shown that the Ultra-Weak Variational Formulation is in fact a subset of the present discontinuous Galerkin method. A special extension of the method is devised in order to deal with singular solutions generated by point sources like monopoles or dipoles. Aeroacoustic problems with non-uniform flows are also considered and results are presented for the sound radiated from a two-dimensional jet.