Computer Methods in Applied Mechanics and Engineering
Computer Methods in Applied Mechanics and Engineering
Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
A class of implicit upwind schemes for Euler simulations with unstructured meshes
Journal of Computational Physics
Optimum positive linear schemes for advection in two and three dimensions
SIAM Journal on Numerical Analysis
On essentially non-oscillatory schemes on unstructured meshes: analysis and implementation
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Journal of Computational Physics
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
SIAM Journal on Numerical Analysis
Weighted essentially non-oscillatory schemes on triangular meshes
Journal of Computational Physics
Toward the ultimate conservative scheme: following the quest
Journal of Computational Physics
A residual-based compact scheme for the compressible Navier-Stokes equations
Journal of Computational Physics
Residual Distribution Schemes for Conservation Laws via Adaptive Quadrature
SIAM Journal on Scientific Computing
High Order Fluctuation Schemes on Triangular Meshes
Journal of Scientific Computing
Journal of Computational Physics
A second-order-accurate monotone implicit fluctuation splitting scheme for unsteady problems
Journal of Computational Physics
Residual distribution for general time-dependent conservation laws
Journal of Computational Physics
Journal of Computational Physics
Essentially non-oscillatory Residual Distribution schemes for hyperbolic problems
Journal of Computational Physics
Well-balanced finite volume evolution Galerkin methods for the shallow water equations
Journal of Computational Physics
Third-order-accurate fluctuation splitting schemes for unsteady hyperbolic problems
Journal of Computational Physics
Journal of Computational Physics
Non-oscillatory third order fluctuation splitting schemes for steady scalar conservation laws
Journal of Computational Physics
Finite volume evolution Galerkin (FVEG) methods for three-dimensional wave equation system
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
A class of residual distribution schemes and their relation to relaxation systems
Journal of Computational Physics
Discontinuous fluctuation distribution
Journal of Computational Physics
Stabilized residual distribution for shallow water simulations
Journal of Computational Physics
Explicit Runge-Kutta residual distribution schemes for time dependent problems: Second order case
Journal of Computational Physics
An Example of High Order Residual Distribution Scheme Using non-Lagrange Elements
Journal of Scientific Computing
Hi-index | 31.51 |
The aim of this paper is to construct upwind residual distribution schemes for the time accurate solution of hyperbolic conservation laws. To do so, we evaluate a space-time fluctuation based on a space-time approximation of the solution and develop new residual distribution schemes which are extensions of classical steady upwind residual distribution schemes. This method has been applied to the solution of scalar advection equation and to the solution of the compressible Euler equations both in two space dimensions. The first version of the scheme is shown to be, at least in its first order version, unconditionally energy stable and possibly conditionally monotonicity preserving. Using an idea of Csik et al. [Space-time residual distribution schemes for hyperbolic conservation laws, 15th AIAA Computational Fluid Dynamics Conference, Anahein, CA, USA, AIAA 2001-2617, June 2001], we modify the formulation to end up with a scheme that is unconditionally energy stable and unconditionally monotonicity preserving. Several numerical examples are shown to demonstrate the stability and accuracy of the method.