Time dependent boundary conditions for hyperbolic systems
Journal of Computational Physics
Journal of Computational Physics
On the rotation and skew-symmetric forms for incompressible flow simulations
Applied Numerical Mathematics - Special issue: Transition to turbulence
SIAM Journal on Scientific and Statistical Computing
The stability of numerical boundary treatments for compact high-order finite-difference schemes
Journal of Computational Physics
Summation by parts for finite difference approximations for d/dx
Journal of Computational Physics
Immersed Interface Methods for Stokes Flow with Elastic Boundaries or Surface Tension
SIAM Journal on Scientific Computing
A hybrid method for moving interface problems with application to the Hele-Shaw flow
Journal of Computational Physics
SIAM Journal on Numerical Analysis
A Fast Iterative Algorithm for Elliptic Interface Problems
SIAM Journal on Numerical Analysis
Preconditioned multigrid methods for unsteady incompressible flows
Journal of Computational Physics
SIAM Journal on Scientific Computing
A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method)
Journal of Computational Physics
SIAM Journal on Numerical Analysis
An immersed boundary method with formal second-order accuracy and reduced numerical viscosity
Journal of Computational Physics
Journal of Computational Physics
The immersed interface method for the Navier-Stokes equations with singular forces
Journal of Computational Physics
A front-tracking method for the computations of multiphase flow
Journal of Computational Physics
An immersed-boundary finite-volume method for simulations of flow in complex geometries
Journal of Computational Physics
An Immersed Interface Method for Incompressible Navier-Stokes Equations
SIAM Journal on Scientific Computing
High-order FDTD methods via derivative matching for Maxwell's equations with material interfaces
Journal of Computational Physics
Higher entropy conservation and numerical stability of compressible turbulence simulations
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
The Explicit Simplified Interface Method for Compressible Multicomponent Flows
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Well-Posed Boundary Conditions for the Navier--Stokes Equations
SIAM Journal on Numerical Analysis
A Second Order Accurate Embedded Boundary Method for the Wave Equation with Dirichlet Data
SIAM Journal on Scientific Computing
An immersed interface method for simulating the interaction of a fluid with moving boundaries
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Unconditionally stable discretizations of the immersed boundary equations
Journal of Computational Physics
The immersed interface method for two-dimensional heat-diffusion equations with singular own sources
Applied Numerical Mathematics
The accuracy of the modified ghost fluid method for gas--gas Riemann problem
Applied Numerical Mathematics
Matched interface and boundary (MIB) method for elliptic problems with sharp-edged interfaces
Journal of Computational Physics
An immersed boundary method for complex incompressible flows
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A sharp interface immersed boundary method for compressible viscous flows
Journal of Computational Physics
A coupling interface method for elliptic interface problems
Journal of Computational Physics
An immersed boundary method for compressible flows using local grid refinement
Journal of Computational Physics
The immersed boundary method: A projection approach
Journal of Computational Physics
Journal of Computational Physics
Three-dimensional matched interface and boundary (MIB) method for treating geometric singularities
Journal of Computational Physics
Hi-index | 31.45 |
A numerical method to solve the compressible Navier-Stokes equations around objects of arbitrary shape using Cartesian grids is described. The approach considered here uses an embedded geometry representation of the objects and approximate the governing equations with a low numerical dissipation centered finite-difference discretization. The method is suitable for compressible flows without shocks and can be classified as an immersed interface method. The objects are sharply captured by the Cartesian mesh by appropriately adapting the discretization stencils around the irregular grid nodes, located around the boundary. In contrast with available methods, no jump conditions are used or explicitly derived from the boundary conditions, although a number of elements are adopted from previous immersed interface approaches. A new element in the present approach is the use of the summation-by-parts formalism to develop stable non-stiff first-order derivative approximations at the irregular grid points. Second-order derivative approximations, as those appearing in the transport terms, can be stiff when irregular grid points are located too close to the boundary. This is addressed using a semi-implicit time integration method. Moreover, it is shown that the resulting implicit equations can be solved explicitly in the case of constant transport properties. Convergence studies are performed for a rotating cylinder and vortex shedding behind objects of varying shapes at different Mach and Reynolds numbers.