Total-variation-diminishing time discretizations
SIAM Journal on Scientific and Statistical Computing
Journal of Computational Physics
High-order accurate discontinuous finite element solution of the 2D Euler equations
Journal of Computational Physics
From Electrostatics to Almost Optimal Nodal Sets for Polynomial Interpolation in a Simplex
SIAM Journal on Numerical Analysis
Exact integrations of polynomials and symmetric quadrature formulas over arbitrary polyhedral grids
Journal of Computational Physics
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
A staggered-grid multidomain spectral method for the compressible Navier-Stokes equations
Journal of Computational Physics
The Mathematica book (4th edition)
The Mathematica book (4th edition)
Spectral (finite) volume method for conservation laws on unstructured grids: basic formulation
Journal of Computational Physics
A New Class of Optimal High-Order Strong-Stability-Preserving Time Discretization Methods
SIAM Journal on Numerical Analysis
Journal of Computational Physics
An upwind finite difference scheme for meshless solvers
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Spectral difference method for unstructured grids I: basic formulation
Journal of Computational Physics
Short Note: On the connection between the spectral volume and the spectral difference method
Journal of Computational Physics
On the Stability and Accuracy of the Spectral Difference Method
Journal of Scientific Computing
High Order Strong Stability Preserving Time Discretizations
Journal of Scientific Computing
Spectral difference method for compressible flow on unstructured grids with mixed elements
Journal of Computational Physics
High order multi-moment constrained finite volume method. Part I: Basic formulation
Journal of Computational Physics
Multi-dimensional limiting process for hyperbolic conservation laws on unstructured grids
Journal of Computational Physics
Journal of Computational Physics
An implicit high-order spectral difference approach for large eddy simulation
Journal of Computational Physics
A Proof of the Stability of the Spectral Difference Method for All Orders of Accuracy
Journal of Scientific Computing
Journal of Computational Physics
A New Class of High-Order Energy Stable Flux Reconstruction Schemes
Journal of Scientific Computing
Journal of Computational Physics
A New Class of High-Order Energy Stable Flux Reconstruction Schemes for Triangular Elements
Journal of Scientific Computing
Journal of Scientific Computing
An optimized spectral difference scheme for CAA problems
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
High-order solution-adaptive central essentially non-oscillatory (CENO) method for viscous flows
Journal of Computational Physics
Hi-index | 0.07 |
An efficient, high-order, conservative method named the spectral difference method has been developed recently for conservation laws on unstructured grids. It combines the best features of structured and unstructured grid methods to achieve high-computational efficiency and geometric flexibility; it utilizes the concept of discontinuous and high-order local representations to achieve conservation and high accuracy; and it is based on the finite-difference formulation for simplicity. The method is easy to implement since it does not involve surface or volume integrals. Universal reconstructions are obtained by distributing solution and flux points in a geometrically similar manner for simplex cells. In this paper, the method is further extended to nonlinear systems of conservation laws, the Euler equations. Accuracy studies are performed to numerically verify the order of accuracy. In order to capture both smooth feature and discontinuities, monotonicity limiters are implemented, and tested for several problems in one and two dimensions. The method is more efficient than the discontinuous Galerkin and spectral volume methods for unstructured grids.