Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Journal of Computational Physics
Journal of Computational Physics
Parallel, adaptive finite element methods for conservation laws
Proceedings of the third ARO workshop on Adaptive methods for partial differential equations
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
A MUSCL method satisfying all the numerical entropy inequalities
Mathematics of Computation
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
Journal of Computational Physics
Weighted essentially non-oscillatory schemes on triangular meshes
Journal of Computational Physics
Journal of Computational Physics
A problem-independent limiter for high-order Runge—Kutta discontinuous Galerkin methods
Journal of Computational Physics
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
Journal of Computational Physics
A technique of treating negative weights in WENO schemes
Journal of Computational Physics
Journal of Computational Physics
Runge--Kutta Discontinuous Galerkin Method Using WENO Limiters
SIAM Journal on Scientific Computing
Locally Divergence-Free Discontinuous Galerkin Methods for MHD Equations
Journal of Scientific Computing
Locally divergence-free discontinuous Galerkin methods for MHD equations
Journal of Scientific Computing
Building Blocks for Arbitrary High Order Discontinuous Galerkin Schemes
Journal of Scientific Computing
Viscous stabilization of discontinuous Galerkin solutions of hyperbolic conservation laws
Applied Numerical Mathematics - The third international conference on the numerical solutions of volterra and delay equations, May 2004, Tempe, AZ
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Arbitrary High-Order Discontinuous Galerkin Schemes for the Magnetohydrodynamic Equations
Journal of Scientific Computing
A Runge-Kutta discontinuous Galerkin method for viscous flow equations
Journal of Computational Physics
A Hermite WENO-based limiter for discontinuous Galerkin method on unstructured grids
Journal of Computational Physics
A Hermite upwind WENO scheme for solving hyperbolic conservation laws
Journal of Computational Physics
Runge-Kutta discontinuous Galerkin method using WENO limiters II: Unstructured meshes
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Towards a compact high-order method for non-linear hyperbolic systems, II. The Hermite-HLLC scheme
Journal of Computational Physics
High order multi-moment constrained finite volume method. Part I: Basic formulation
Journal of Computational Physics
Journal of Computational Physics
Journal of Scientific Computing
Journal of Computational Physics
Viscous stabilization of discontinuous Galerkin solutions of hyperbolic conservation laws
Applied Numerical Mathematics
Journal of Computational Physics
A weighted-integral based scheme
Journal of Computational Physics
A high-order gas-kinetic Navier-Stokes flow solver
Journal of Computational Physics
Approximation error of the Lagrange reconstructing polynomial
Journal of Approximation Theory
A Speed-Up Strategy for Finite Volume WENO Schemes for Hyperbolic Conservation Laws
Journal of Scientific Computing
Journal of Computational Physics
Journal of Computational Physics
A class of hybrid DG/FV methods for conservation laws II: Two-dimensional cases
Journal of Computational Physics
A simple weighted essentially nonoscillatory limiter for Runge-Kutta discontinuous Galerkin methods
Journal of Computational Physics
Journal of Scientific Computing
Hermite WENO schemes for Hamilton-Jacobi equations on unstructured meshes
Journal of Computational Physics
Hi-index | 31.55 |
In this paper, a class of fifth-order weighted essentially non-oscillatory (WENO) schemes based on Hermite polynomials, termed HWENO (Hermite WENO) schemes, for solving one-dimensional nonlinear hyperbolic conservation law systems is presented. The construction of HWENO schemes is based on a finite volume formulation, Hermite interpolation, and nonlinearly stable Runge-Kutta methods. The idea of the reconstruction in the HWENO schemes comes from the original WENO schemes, however both the function and its first derivative values are evolved in time and used in the reconstruction, while only the function values are evolved and used in the original WENO schemes. Comparing with the original WENO schemes of Liu et al. [J. Comput. Phys. 115 (1994) 200] and Jiang and Shu [J. Comput. Phys. 126 (1996) 202], one major advantage of HWENO schemes is its compactness in the reconstruction. For example, five points are needed in the stencil for a fifth-order WENO (WENO5) reconstruction, while only three points are needed for a fifth-order HWENO (HWENO5) reconstruction. For this reason, the HWENO finite volume methodology is more suitable to serve as limiters for the Runge-Kutta discontinuous Galerkin (RKDG) methods, than the original WENO finite volume methodology. Such applications in one space dimension is also developed in this paper.