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
Characteristic Galerkin methods for scalar conservation laws in one dimension
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
High-resolution conservative algorithms for advection in incompressible flow
SIAM Journal on Numerical Analysis
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
A high-order discontinuous Galerkin method for 2D incompressible flows
Journal of Computational Physics
Conservative numerical schemes for the Vlasov equation
Journal of Computational Physics
A characteristic Galerkin method for discrete Boltzmann equation
Journal of Computational Physics
A technique of treating negative weights in WENO schemes
Journal of Computational Physics
Journal of Computational Physics
Semi-Lagrangian schemes for the Vlasov equation on an unstructured mesh of phase space
Journal of Computational Physics
Nonoscillatory Interpolation Methods Applied to Vlasov-Based Models
SIAM Journal on Scientific Computing
High Order Strong Stability Preserving Time Discretizations
Journal of Scientific Computing
A conservative high order semi-Lagrangian WENO method for the Vlasov equation
Journal of Computational Physics
Hermite Spline Interpolation on Patches for Parallelly Solving the Vlasov-Poisson Equation
International Journal of Applied Mathematics and Computer Science - Scientific Computation for Fluid Mechanics and Hyperbolic Systems
On maximum-principle-satisfying high order schemes for scalar conservation laws
Journal of Computational Physics
An Eulerian-Lagrangian WENO finite volume scheme for advection problems
Journal of Computational Physics
Journal of Computational Physics
Hybrid semi-Lagrangian finite element-finite difference methods for the Vlasov equation
Journal of Computational Physics
A level set two-way wave equation approach for Eulerian interface tracking
Journal of Computational Physics
Stability of Some Generalized Godunov Schemes With Linear High-Order Reconstructions
Journal of Scientific Computing
Hi-index | 31.48 |
In this paper, we propose a semi-Lagrangian finite difference formulation for approximating conservative form of advection equations with general variable coefficients. Compared with the traditional semi-Lagrangian finite difference schemes [5,25], which approximate the advective form of the equation via direct characteristics tracing, the scheme proposed in this paper approximates the conservative form of the equation. This essential difference makes the proposed scheme naturally conservative for equations with general variable coefficients. The proposed conservative semi-Lagrangian finite difference framework is coupled with high order essentially non-oscillatory (ENO) or weighted ENO (WENO) reconstructions to achieve high order accuracy in smooth parts of the solution and to capture sharp interfaces without introducing spurious oscillations. The scheme is extended to high dimensional problems by Strang splitting. The performance of the proposed schemes is demonstrated by linear advection, rigid body rotation, swirling deformation, and two dimensional incompressible flow simulation in the vorticity stream-function formulation. As the information is propagating along characteristics, the proposed scheme does not have the CFL time step restriction of the Eulerian method, allowing for a more efficient numerical realization for many application problems.