The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
SIAM Journal on Scientific and Statistical Computing
Dispersion-relation-preserving finite difference schemes for computational acoustics
Journal of Computational Physics
Low-dissipation and low-dispersion Runge-Kutta schemes for computational acoustics
Journal of Computational Physics
2N-storage low dissipation and dispersion Runge-Kutta schemes for computational acoustics
Journal of Computational Physics
Analysis of central and upwind compact schemes
Journal of Computational Physics
A family of low dispersive and low dissipative explicit schemes for flow and noise computations
Journal of Computational Physics
A Comparative Study of Time Advancement Methods for Solving Navier–Stokes Equations
Journal of Scientific Computing
High Accuracy Compact Schemes and Gibbs' Phenomenon
Journal of Scientific Computing
Short note: a new minimum storage Runge-Kutta scheme for computational acoustics
Journal of Computational Physics
High Accuracy Schemes for DNS and Acoustics
Journal of Scientific Computing
Symmetrized compact scheme for receptivity study of 2D transitional channel flow
Journal of Computational Physics
Journal of Computational Physics
Performance analysis and optimization of finite-difference schemes for wave propagation problems
Journal of Computational Physics
Short Note: Error dynamics: Beyond von Neumann analysis
Journal of Computational Physics
A new combined stable and dispersion relation preserving compact scheme for non-periodic problems
Journal of Computational Physics
A general strategy for the optimization of Runge-Kutta schemes for wave propagation phenomena
Journal of Computational Physics
Journal of Computational Physics
Finite difference schemes for long-time integration
Journal of Computational Physics
Analysis of anisotropy of numerical wave solutions by high accuracy finite difference methods
Journal of Computational Physics
A linear focusing mechanism for dispersive and non-dispersive wave problems
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.46 |
In this paper we examine the constrained optimization of explicit Runge-Kutta (RK) schemes coupled with central spatial discretization schemes to solve the one-dimensional convection equation. The constraints are defined with respect to the correct error propagation equation which goes beyond the traditional von Neumann analysis developed in Sengupta et al. [T.K. Sengupta, A. Dipankar, P. Sagaut, Error dynamics: beyond von Neumann analysis, J. Comput. Phys. 226 (2007) 1211-1218]. The efficiency of these optimal schemes is demonstrated for the one-dimensional convection problem and also by solving the Navier-Stokes equations for a two-dimensional lid-driven cavity (LDC) problem. For the LDC problem, results for Re=1000 are compared with results using spectral methods in Botella and Peyret [O. Botella, R. Peyret, Benchmark spectral results on the lid-driven cavity flow, Comput. Fluids 27 (1998) 421-433] to calibrate the method in solving the steady state problem. We also report the results of the same flow at Re=10,000 and compare them with some recent results to establish the correctness and accuracy of the scheme for solving unsteady flow problems. Finally, we also compare our results for a wave-packet propagation problem with another method developed for computational aeroacoustics.