Journal of Computational Physics
A three-dimensional computational method for blood flow in the heart. II. contractile fibers
Journal of Computational Physics
Improved volume conservation in the computation of flows with immersed elastic boundaries
Journal of Computational Physics
SIAM Journal on Numerical Analysis
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 Cartesian Grid Projection Method for the Incompressible Euler Equations in Complex Geometries
SIAM Journal on Scientific Computing
A New Mixed Finite Element Formulation and the MAC Method for the Stokes Equations
SIAM Journal on Numerical Analysis
An adaptive version of the immersed boundary method
Journal of Computational Physics
A boundary condition capturing method for Poisson's equation on irregular domains
Journal of Computational Physics
A Boundary Condition Capturing Method for Multiphase Incompressible Flow
Journal of Scientific Computing
The immersed interface method for the Navier-Stokes equations with singular forces
Journal of Computational Physics
An Immersed Interface Method for Incompressible Navier-Stokes Equations
SIAM Journal on Scientific Computing
A fast solver for the Stokes equations with distributed forces in complex geometries
Journal of Computational Physics
Journal of Computational Physics
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
An adaptive, formally second order accurate version of the immersed boundary method
Journal of Computational Physics
A fast variational framework for accurate solid-fluid coupling
ACM SIGGRAPH 2007 papers
Journal of Computational Physics
Fictitious Domain Approach Via Lagrange Multipliers with Least Squares Spectral Element Method
Journal of Scientific Computing
Fictitious Domain approach with hp-finite element approximation for incompressible fluid flow
Journal of Computational Physics
Mimetic finite difference method for the Stokes problem on polygonal meshes
Journal of Computational Physics
An efficient fluid-solid coupling algorithm for single-phase flows
Journal of Computational Physics
SIAM Journal on Scientific Computing
Tether Force Constraints in Stokes Flow by the Immersed Boundary Method on a Periodic Domain
SIAM Journal on Scientific Computing
An Eulerian method for multi-component problems in non-linear elasticity with sliding interfaces
Journal of Computational Physics
A second order virtual node method for elliptic problems with interfaces and irregular domains
Journal of Computational Physics
An Eulerian hybrid WENO centered-difference solver for elastic-plastic solids
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.45 |
We present numerical methods for the solution of the Stokes equations that handle interfacial discontinuities, discontinuous material properties and irregular domains. The discretization couples a Lagrangian representation of the material interface with Eulerian representations of the fluid velocity and pressure. The methods are efficient, easy to implement and yield discretely divergence-free velocities that are second order accurate in L^~. For the special case of continuous fluid viscosity, we present a method that decouples the Stokes equations into three Poisson interface problems which we use the techniques in Bedrossian (2010) [1] to solve. We also solve a fourth Poisson equation to enforce a discrete divergence free condition in this case. We discretize all equations using an embedded approach on a uniform MAC grid employing virtual nodes and duplicated cells at the interfaces. These additional degrees of freedom allow for accurate resolution of discontinuities in the fluid stress at the material interface. In the case of discontinuous viscosity, we require a Lagrange multiplier term to enforce continuity of the fluid velocity. We provide a novel discretization of this term that accurately resolves constant pressure null modes. We show that the accurate resolution of these modes significantly improves performance. The discrete coupled equations for the velocity, pressure and Lagrange multipliers are in the form of a symmetric KKT system. However, if both fluids have the same viscosity then all four linear systems involved are symmetric positive definite with three of the four having the standard 5-point Laplace stencil everywhere. Numerical results indicate second order accuracy for the velocities and first order accuracy for the pressure in the general case. For the continuous viscosity case, numerical results indicate second order accuracy for both velocities and pressure.