Total-variation-diminishing time discretizations
SIAM Journal on Scientific and Statistical Computing
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Journal of Computational Physics
Journal of Computational Physics
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
A conservative staggered-grid Chebyshev multidomain method for compressible flows
Journal of Computational Physics
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
The constrained interpolation profile method for multiphase analysis
Journal of Computational Physics
Completely conservative and oscillationless semi-Lagrangian schemes for advection transportation
Journal of Computational Physics
Spectral (finite) volume method for conservation laws on unstructured grids: basic formulation
Journal of Computational Physics
ADER: Arbitrary High Order Godunov Approach
Journal of Scientific Computing
Journal of Computational Physics
Resolution of high order WENO schemes for complicated flow structures
Journal of Computational Physics
Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Conservation Laws
Journal of Computational Physics
Journal of Computational Physics
Derivative Riemann solvers for systems of conservation laws and ADER methods
Journal of Computational Physics
Spectral difference method for unstructured grids I: basic formulation
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
Journal of Computational Physics
Shallow water model on cubed-sphere by multi-moment finite volume method
Journal of Computational Physics
Numerical simulations of free-interface fluids by a multi-integrated moment method
Computers and Structures
Journal of Computational Physics
A high-order gas-kinetic Navier-Stokes flow solver
Journal of Computational Physics
Journal of Computational Physics
Journal of Scientific Computing
Hi-index | 31.46 |
A new high-order finite volume method based on local reconstruction is presented in this paper. The method, so-called the multi-moment constrained finite volume (MCV) method, uses the point values defined within single cell at equally spaced points as the model variables (or unknowns). The time evolution equations used to update the unknowns are derived from a set of constraint conditions imposed on multi kinds of moments, i.e. the cell-averaged value and the point-wise value of the state variable and its derivatives. The finite volume constraint on the cell-average guarantees the numerical conservativeness of the method. Most constraint conditions are imposed on the cell boundaries, where the numerical flux and its derivatives are solved as general Riemann problems. A multi-moment constrained Lagrange interpolation reconstruction for the demanded order of accuracy is constructed over single cell and converts the evolution equations of the moments to those of the unknowns. The presented method provides a general framework to construct efficient schemes of high orders. The basic formulations for hyperbolic conservation laws in 1- and 2D structured grids are detailed with the numerical results of widely used benchmark tests.