Author(s): Ramya Raghavendra
Journal: CFD Letters
ISSN 2180-1363
Volume: 3;
Issue: 2;
Start page: 74;
Date: 2011;
Original page
Keywords: Spectral volume method | LDG | Penalty formulation | Linear Fourier analysis
ABSTRACT
In this paper, we present an interior penalty formulation for solving equations containing third spatial derivative terms, in the context of a high order spectral volume method. The motivation for this approach comes from the “penalization method” (Kannan R, Wang Z.J., “A Study of Viscous Flux Formulations for a p-Multigrid Spectral Volume Navier Stokes Solver, “Journal of Scientific Computing, 41(2), 2009, 165 - 199) developed for discretizing the second order viscous fluxes. A linear Fourier analysis was performed to compare and contrast the dispersion and the dissipation properties of the new formulation and the existing LDG (Local Discontinuous Galerkin) formulation. The analyses performed on the linear and the cubic partitions showed improvement over the traditional LDG formulation. The analysis performed on the quadratic partition showed significant dispersion, when compared to the LDG scheme. The new formulation is easy to implement and is highly symmetrical. Numerical experiments were conducted and the results were in accord with the analysis results. In general, the formulation is general and can be used even for higher dimension problems.
Journal: CFD Letters
ISSN 2180-1363
Volume: 3;
Issue: 2;
Start page: 74;
Date: 2011;
Original page
Keywords: Spectral volume method | LDG | Penalty formulation | Linear Fourier analysis
ABSTRACT
In this paper, we present an interior penalty formulation for solving equations containing third spatial derivative terms, in the context of a high order spectral volume method. The motivation for this approach comes from the “penalization method” (Kannan R, Wang Z.J., “A Study of Viscous Flux Formulations for a p-Multigrid Spectral Volume Navier Stokes Solver, “Journal of Scientific Computing, 41(2), 2009, 165 - 199) developed for discretizing the second order viscous fluxes. A linear Fourier analysis was performed to compare and contrast the dispersion and the dissipation properties of the new formulation and the existing LDG (Local Discontinuous Galerkin) formulation. The analyses performed on the linear and the cubic partitions showed improvement over the traditional LDG formulation. The analysis performed on the quadratic partition showed significant dispersion, when compared to the LDG scheme. The new formulation is easy to implement and is highly symmetrical. Numerical experiments were conducted and the results were in accord with the analysis results. In general, the formulation is general and can be used even for higher dimension problems.
