Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
The discrete continuity equation in primitive variable solutions of incompressible flow
Journal of Computational Physics
A level set approach for computing solutions to incompressible two-phase flow
Journal of Computational Physics
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
Fully conservative higher order finite difference schemes for incompressible flow
Journal of Computational Physics
Computation of solid-liquid phase fronts in the sharp interface limit on fixed grids
Journal of Computational Physics
An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries
Journal of Computational Physics
Combined immmersed-boundary finite-difference methods for three-dimensional complex flow simulations
Journal of Computational Physics
Active control and drag optimization for flow past a circular cylinder
Journal of Computational Physics
Journal of Computational Physics
Level set methods: an overview and some recent results
Journal of Computational Physics
A sharp interface Cartesian Ggid method for simulating flows with complex moving boundaries: 345
Journal of Computational Physics
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
A second-order-accurate symmetric discretization of the Poisson equation on irregular domains
Journal of Computational Physics
Symmetry-preserving discretization of turbulent flow
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Immersed boundary method for flow around an arbitrarily moving body
Journal of Computational Physics
Journal of Computational Physics
Journal of Scientific Computing
Journal of Computational Physics
An improved immersed boundary method with direct forcing for the simulation of particle laden flows
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.46 |
This paper concerns the development of a new Cartesian grid/immersed boundary (IB) method for the computation of incompressible viscous flows in two-dimensional irregular geometries. In IB methods, the computational grid is not aligned with the irregular boundary, and of upmost importance for accuracy and stability is the discretization in cells which are cut by the boundary, the so-called ''cut-cells''. In this paper, we present a new IB method, called the LS-STAG method, which is based on the MAC method for staggered Cartesian grids and where the irregular boundary is sharply represented by its level-set function. This implicit representation of the immersed boundary enables us to calculate efficiently the geometry parameters of the cut-cells. We have achieved a novel discretization of the fluxes in the cut-cells by enforcing the strict conservation of total mass, momentum and kinetic energy at the discrete level. Our discretization in the cut-cells is consistent with the MAC discretization used in Cartesian fluid cells, and has the ability to preserve the five-point Cartesian structure of the stencil, resulting in a highly computationally efficient method. The accuracy and robustness of our method is assessed on canonical flows at low to moderate Reynolds number: Taylor-Couette flow, flows past a circular cylinder, including the case where the cylinder has forced oscillatory rotations. Finally, we will extend the LS-STAG method to the handling of moving immersed boundaries and present some results for the transversely oscillating cylinder flow in a free-stream.