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
SIAM Journal on Scientific Computing
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Difference Approximations for the Second Order Wave Equation
SIAM Journal on Numerical Analysis
H-Box Methods for the Approximation of Hyperbolic Conservation Laws on Irregular Grids
SIAM Journal on Numerical Analysis
Resolution of high order WENO schemes for complicated flow structures
Journal of Computational Physics
Multidomain WENO Finite Difference Method with Interpolation at Subdomain Interfaces
Journal of Scientific Computing
Difference Approximations of the Neumann Problem for the Second Order Wave Equation
SIAM Journal on Numerical Analysis
A Second Order Accurate Embedded Boundary Method for the Wave Equation with Dirichlet Data
SIAM Journal on Scientific Computing
High-order accurate implementation of solid wall boundary conditions in curved geometries
Journal of Computational Physics
High Order Strong Stability Preserving Time Discretizations
Journal of Scientific Computing
Journal of Scientific Computing
A high order moving boundary treatment for compressible inviscid flows
Journal of Computational Physics
Uniformly Accurate Discontinuous Galerkin Fast Sweeping Methods for Eikonal Equations
SIAM Journal on Scientific Computing
Efficient implementation of high order inverse Lax-Wendroff boundary treatment for conservation laws
Journal of Computational Physics
3DFLUX: A high-order fully three-dimensional flux integral solver for the scalar transport equation
Journal of Computational Physics
Hi-index | 31.46 |
We develop a high order finite difference numerical boundary condition for solving hyperbolic conservation laws on a Cartesian mesh. The challenge results from the wide stencil of the interior high order scheme and the fact that the boundary intersects the grids in an arbitrary fashion. Our method is based on an inverse Lax-Wendroff procedure for the inflow boundary conditions. We repeatedly use the partial differential equation to write the normal derivatives to the inflow boundary in terms of the time derivatives and the tangential derivatives. With these normal derivatives, we can then impose accurate values of ghost points near the boundary by a Taylor expansion. At outflow boundaries, we use Lagrange extrapolation or least squares extrapolation if the solution is smooth, or a weighted essentially non-oscillatory (WENO) type extrapolation if a shock is close to the boundary. Extensive numerical examples are provided to illustrate that our method is high order accurate and has good performance when applied to one and two-dimensional scalar or system cases with the physical boundary not aligned with the grids and with various boundary conditions including the solid wall boundary condition. Additional numerical cost due to our boundary treatment is discussed in some of the examples.