Surface tension and viscosity with Lagrangian hydrodynamics on a triangular mesh
Journal of Computational Physics
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
High-order essentially nonsocillatory schemes for Hamilton-Jacobi equations
SIAM Journal on Numerical Analysis
A front-tracking method for viscous, incompressible, multi-fluid flows
Journal of Computational Physics
Computations of multi-fluid flows
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
A 3D adaptive mesh refinement algorithm for multimaterial gas dynamics
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
An adaptively refined Cartesian mesh solver for the Euler equations
Journal of Computational Physics
A level set approach for computing solutions to incompressible two-phase flow
Journal of Computational Physics
A fast level set method for propagating interfaces
Journal of Computational Physics
An adaptive Cartesian grid method for unsteady compressible flow in irregular regions
Journal of Computational Physics
Two-dimensional front tracking based on high resolution wave propagation methods
Journal of Computational Physics
A Cartesian Grid Projection Method for the Incompressible Euler Equations in Complex Geometries
SIAM Journal on Scientific Computing
Three-Dimensional Front Tracking
SIAM Journal on Scientific Computing
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
A Discontinuous Galerkin Finite Element Method for Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
A Simple Method for Compressible Multifluid Flows
SIAM Journal on Scientific Computing
An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries
Journal of Computational Physics
Journal of Computational Physics
A sharp interface Cartesian Ggid method for simulating flows with complex moving boundaries: 345
Journal of Computational Physics
Conservative Front Tracking with Improved Accuracy
SIAM Journal on Numerical Analysis
Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws
Applied Numerical Mathematics - Special issue: Workshop on innovative time integrators for PDEs
Journal of Scientific Computing
Space-time discontinuous Galerkin method for the compressible Navier-Stokes equations
Journal of Computational Physics
Journal of Computational Physics
Space-time discontinuous Galerkin method for advection-diffusion problems on time-dependent domains
Applied Numerical Mathematics
Space-time discontinuous Galerkin finite element method for shallow water flows
Journal of Computational and Applied Mathematics
Space-time discontinuous Galerkin method for nonlinear water waves
Journal of Computational Physics
hpGEM---A software framework for discontinuous Galerkin finite element methods
ACM Transactions on Mathematical Software (TOMS)
A Hermite WENO-based limiter for discontinuous Galerkin method on unstructured grids
Journal of Computational Physics
Space-time discontinuous Galerkin discretization of rotating shallow water equations
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Adaptive moment-of-fluid method
Journal of Computational Physics
Journal of Computational Physics
A ghost fluid method for compressible reacting flows with phase change
Journal of Computational Physics
Towards front-tracking based on conservation in two space dimensions III, tracking interfaces
Journal of Computational Physics
Hi-index | 31.46 |
A novel numerical method for two-fluid flow computations is presented, which combines the space-time discontinuous Galerkin finite element discretization with the level set method and cut-cell based interface tracking. The space-time discontinuous Galerkin (STDG) finite element method offers high accuracy, an inherent ability to handle discontinuities and a very local stencil, making it relatively easy to combine with local hp-refinement. The front tracking is incorporated via cut-cell mesh refinement to ensure a sharp interface between the fluids. To compute the interface dynamics the level set method (LSM) is used because of its ability to deal with merging and breakup. Also, the LSM is easy to extend to higher dimensions. Small cells arising from the cut-cell refinement are merged to improve the stability and performance. The interface conditions are incorporated in the numerical flux at the interface and the STDG discretization ensures that the scheme is conservative as long as the numerical fluxes are conservative. The numerical method is applied to one and two dimensional two-fluid test problems using the Euler equations.