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
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
Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
Approximate Riemann solvers, parameter vectors, and difference schemes
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
High resolution schemes for hyperbolic conservation laws
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
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
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Short note: a convexity preserving scheme for conservative advection transport
Journal of Computational Physics
Numerical simulations of free-interface fluids by a multi-integrated moment method
Computers and Structures
Shallow water model on cubed-sphere by multi-moment finite volume method
Journal of Computational Physics
High order multi-moment constrained finite volume method. Part I: Basic formulation
Journal of Computational Physics
The use of PDE centres in the local RBF Hermitian method for 3D convective-diffusion problems
Journal of Computational Physics
Journal of Computational Physics
A multi-moment finite volume formulation for shallow water equations on unstructured mesh
Journal of Computational Physics
Journal of Computational Physics
Multi-moment advection scheme for Vlasov simulations
Journal of Computational Physics
Multi-moment advection scheme in three dimension for Vlasov simulations of magnetized plasma
Journal of Computational Physics
Hi-index | 31.49 |
An accurate algorithm for the hyperbolic equations has been proposed by combining the constrained interpolation profile/multi-moment finite volume method (CIP/MM FVM) with the characteristic theory. Two types of moments, i.e. the point value (PV) at cell boundary of each mesh element and the volume-integrated average (VIA) over each mesh cell of a physical field, are treated as the model variables and updated independently in time. The interpolation that uses both PV and VIA is reconstructed for each Riemann invariant of the hyperbolic conservation laws. The PVs are then updated by semi-Lagrangian schemes along the characteristic curves, while the VIAs are computed by formulations of flux form, where the numerical fluxes are evaluated by averaging the physical fields over the characteristic curves. The Runge-Kutta type schemes are used for integrating the trajectory equations based on the characteristic speeds to improve the accuracy in time. The numerical procedure for the one-dimensional Euler conservation laws is described in detail in this paper. Number of benchmark tests are presented. The numerical results show that the present method is accurate and competitive to other existing methods.