Journal of Computational Physics
A spectral multidomain method for the solution of hyperbolic systems
Applied Numerical Mathematics - Special issue in honor of Milt Rose's sixtieth birthday
Total-variation-diminishing time discretizations
SIAM Journal on Scientific and Statistical Computing
Journal of Computational Physics
A conservative staggered-grid Chebyshev multidomain method for compressible flows
Journal of Computational Physics
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 collocation time-domain modeling of diffractive optical elements
Journal of Computational Physics
Spectral (finite) volume method for conservation laws on unstructured grids: basic formulation
Journal of Computational Physics
An Algorithm for Computing Fekete Points in the Triangle
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Nodal high-order methods on unstructured grids
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 II: Extension to the Euler Equations
Journal of Scientific Computing
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
A spectrally refined interface approach for simulating multiphase flows
Journal of Computational Physics
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
ICCS 2009 Proceedings of the 9th International Conference on Computational Science
Journal of Computational Physics
An implicit high-order spectral difference approach for large eddy simulation
Journal of Computational Physics
A high-order gas-kinetic Navier-Stokes flow solver
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
Large-eddy simulation of turbulent channel flows with conservative IDO scheme
Journal of Computational Physics
Insights from von Neumann analysis of high-order flux reconstruction schemes
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 stable interface element scheme for the p-adaptive lifting collocation penalty formulation
Journal of Computational Physics
Journal of Computational Physics
On the Non-linear Stability of Flux Reconstruction Schemes
Journal of Scientific Computing
A New Class of High-Order Energy Stable Flux Reconstruction Schemes for Triangular Elements
Journal of Scientific Computing
An optimized spectral difference scheme for CAA problems
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A p-adaptive LCP formulation for the compressible Navier-Stokes equations
Journal of Computational Physics
A sparse and high-order accurate line-based discontinuous Galerkin method for unstructured meshes
Journal of Computational Physics
Journal of Scientific Computing
Journal of Computational Physics
Journal of Computational Physics
Energy stable flux reconstruction schemes for advection-diffusion problems on triangles
Journal of Computational Physics
Journal of Scientific Computing
Journal of Computational Physics
Hi-index | 31.58 |
A new, high-order, conservative, and efficient method for conservation laws on unstructured grids is developed. It combines the best features of structured and unstructured grid methods to attain 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. Universal reconstructions are obtained by distributing unknown and flux points in a geometrically similar manner for all unstructured cells. Placements of these points with various orders of accuracy are given for the triangular elements. Accuracy studies of the method are carried out with the two-dimensional linear wave equation and Burgers' equation, and each order of accuracy is verified numerically. Numerical solutions of plane electromagnetic waves incident on perfectly conducting circular cylinders are presented and compared with the exact solutions to demonstrate the capability of the method. Excellent agreement has been found. The method is much simpler than the discontinuous Galerkin and spectral volume methods for unstructured grids.