Dispersion-relation-preserving finite difference schemes for computational acoustics
Journal of Computational Physics
Nonlinearly stable compact schemes for shock calculations
SIAM Journal on Numerical Analysis
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Explicit and implicit multidimensional compact high-resolution shock-capturing methods: formulation
Journal of Computational Physics
Second-order upwinding through a characteristic time-step matrix for compressible flow calculations
Journal of Computational Physics
A residual-based compact scheme for the compressible Navier-Stokes equations
Journal of Computational Physics
A family of low dispersive and low dissipative explicit schemes for flow and noise computations
Journal of Computational Physics
Numerical Convergence Study of Nearly Incompressible, Inviscid Taylor-Green Vortex Flow
Journal of Scientific Computing
Residual distribution for general time-dependent conservation laws
Journal of Computational Physics
Multidimensional optimization of finite difference schemes for Computational Aeroacoustics
Journal of Computational Physics
A method for reducing dispersion in convective difference schemes
Journal of Computational Physics
On the design of high order residual-based dissipation for unsteady compressible flows
Journal of Computational Physics
Hi-index | 31.45 |
The wave propagation (spectral) properties of high-order Residual-Based Compact (RBC) discretizations are analyzed to obtain information on the evolution of the Fourier modes supported on a grid of finite size. For these genuinely multidimensional and intrinsically dissipative schemes, a suitable procedure is used to identify the modified wave number associated to their spatial discretization operator, and their dispersive and dissipative behaviors are investigated as functions of a multidimensional wave number. For RBC schemes of higher orders (5 and 7), both dissipation and dispersion errors take very low values up to reduced wave numbers close to the grid resolvability limit, while higher frequencies are efficiently damped out. Thanks to their genuinely multidimensional formulation, RBC schemes conserve good dissipation and dispersion properties even for flow modes that are not aligned with the computational grid. Numerical tests support the theoretical results. Specifically, the study of a complex nonlinear problem dominated by energy transfer from large to small flow scales, the inviscid Taylor-Green vortex flow, confirms numerically the interest of a well-designed RBC dissipation to resolve accurately fine scale flow structures.