Time dependent boundary conditions for hyperbolic systems
Journal of Computational Physics
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
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
A variational level set approach to multiphase motion
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
A simple level set method for solving Stefan problems
Journal of Computational Physics
Preconditioned multigrid methods for unsteady incompressible flows
Journal of Computational Physics
A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method)
Journal of Computational Physics
A PDE-based fast local level set method
Journal of Computational Physics
Journal of Computational Physics
An immersed boundary method with formal second-order accuracy and reduced numerical viscosity
Journal of Computational Physics
Combined immmersed-boundary finite-difference methods for three-dimensional complex flow simulations
Journal of Computational Physics
The immersed interface method for the Navier-Stokes equations with singular forces
Journal of Computational Physics
A sharp interface Cartesian Ggid method for simulating flows with complex moving boundaries: 345
Journal of Computational Physics
An immersed-boundary finite-volume method for simulations of flow in complex geometries
Journal of Computational Physics
Journal of Computational Physics
Semi-Implicit Level Set Methods for Curvature and Surface Diffusion Motion
Journal of Scientific Computing
An Immersed Interface Method for Incompressible Navier-Stokes Equations
SIAM Journal on Scientific Computing
A cartesian grid method for modeling multiple moving objects in 2D incompressible viscous flow
Journal of Computational Physics
Journal of Computational Physics
A ghost-cell immersed boundary method for flow in complex geometry
Journal of Computational Physics
Journal of Computational Physics
A high-wavenumber viscosity for high-resolution numerical methods
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Short Note: Hyperviscosity for shock-turbulence interactions
Journal of Computational Physics
The Explicit Simplified Interface Method for Compressible Multicomponent Flows
SIAM Journal on Scientific Computing
Journal of Computational Physics
SIAM Journal on Scientific Computing
A stencil adaptive algorithm for finite difference solution of incompressible viscous flows
Journal of Computational Physics
Journal of Computational Physics
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 accuracy of the modified ghost fluid method for gas--gas Riemann problem
Applied Numerical Mathematics
An immersed boundary method for complex incompressible flows
Journal of Computational Physics
Journal of Computational and Applied Mathematics
A sharp interface immersed boundary method for compressible viscous flows
Journal of Computational Physics
A conservative level set method for two phase flow II
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
Stability criteria for hybrid difference methods
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A well-conditioned augmented system for solving Navier-Stokes equations in irregular domains
Journal of Computational Physics
Journal of Computational Physics
Short Note: A moving-least-squares reconstruction for embedded-boundary formulations
Journal of Computational Physics
A low numerical dissipation immersed interface method for the compressible Navier-Stokes equations
Journal of Computational Physics
Local adaptive mesh refinement for shock hydrodynamics
Journal of Computational Physics
Hi-index | 31.45 |
An immersed boundary methodology to solve the compressible Navier-Stokes equations around complex geometries in Cartesian fluid dynamics solvers is described. The objective of the new approach is to enable smooth reconstruction of pressure and viscous stresses around the embedded objects without spurious numerical artifacts. A standard level set represents the boundary of the object and defines a fictitious domain into which the flow fields are smoothly extended. Boundary conditions on the surface are enforced by an approach inspired by analytic continuation. Each fluid field is extended independently, constrained only by the boundary condition associated with that field. Unlike most existing methods, no jump conditions or explicit derivation of them from the boundary conditions are required in this approach. Numerical stiffness that arises when the fluid-solid interface is close to grid points of the mesh is addressed by preconditioning. In addition, the embedded geometry technique is coupled with a stable high-order adaptive discretization that is enabled around the object boundary to enhance resolution. The stencils used to transition the order of accuracy of the discretization are derived using the summation-by-parts technique that ensures stability. Applications to shock reflections, shock-ramp interactions, and supersonic and low-Mach number flows over two- and three-dimensional geometries are presented.