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An Efficient hp-Adaptive Strategy for a Level-Set Ghost-Fluid Method
We present an hp-adaptive discretization for a sharp interface model with a level-set ghost-fluid method to simulate compressible multiphase flows....
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A Second-order Modified Ghost Fluid Method (2nd-MGFM) with Discontinuous Galerkin Method for 1-D compressible Multi-medium Problem with Cylindrical and Spherical Symmetry
In this work, we develop the discontinuous Galerkin method to simulate 1-D cylindrical and spherical compressible multi-medium flows with an...
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A narrow band-based dynamic load balancing scheme for the level-set ghost-fluid method
We present a dynamic load balancing scheme for compressible two-phase flows simulations using a high-order level-set ghost-fluid method. The load...
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A Low Mach Number IMEX Flux Splitting for the Level Set Ghost Fluid Method
Considering droplet phenomena at low Mach numbers, large differences in the magnitude of the occurring characteristic waves are presented. As...
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Semi-implicit Finite-Difference Methods for Compressible Gas Dynamics with Curved Boundaries: A Ghost-Point Approach
We present a finite-difference numerical method to solve systems of hyperbolic conservation laws in domains with arbitrary shapes. The curved...
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One- and Multi-dimensional CWENOZ Reconstructions for Implementing Boundary Conditions Without Ghost Cells
We address the issue of point value reconstructions from cell averages in the context of third-order finite volume schemes, focusing in particular on...
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Universal AMG Accelerated Embedded Boundary Method Without Small Cell Stiffness
We develop a universally applicable embedded boundary finite difference method, which results in a symmetric positive definite linear system and does...
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A Conservative Sharp-Interface Numerical Method for Two-dimensional Compressible Two-phase Flows
In this work, a conservative sharp-interface numerical method is developed to simulate compressible two-medium flows with a free interface. In the...
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Ghost State
Ghost state, originally called auxiliary variables [Owicki and Gries, 1976], is a formal technique where the prover adds state (variables or...
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The Cartesian Grid Active Flux Method with Adaptive Mesh Refinement
We present the first implementation of the Active Flux method on adaptively refined Cartesian grids. The Active Flux method is a third order accurate...
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Recent Advances and Complex Applications of the Compressible Ghost-Fluid Method
In this paper, improvements to a level-set ghost-fluid scheme in a high order discontinuous Galerkin framework with finite-volume sub-cells are...
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A Time-Continuous Embedding Method for Scalar Hyperbolic Conservation Laws on Manifolds
A time-continuous (tc-)embedding method is first proposed for solving nonlinear scalar hyperbolic conservation laws with discontinuous solutions...
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Equal Higher Order Analysis of an Unfitted Discontinuous Galerkin Method for Stokes Flow Systems
In this work, we analyze an unfitted discontinuous Galerkin discretization for the numerical solution of the Stokes system based on equal...
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Exponential Time Differencing Method for a Reaction- Diffusion System with Free Boundary
For reaction-diffusion equations in irregular domains with moving boundaries, the numerical stability constraints from the reaction and diffusion...
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Calculation of Seismic Stability of Buildings in the Far North Using the Grid-Characteristic Method
AbstractIn this manuscript we discuss a new modification of the grid-characteristic method for calculating the seismic stability of buildings in the...
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Implicit interpolation method for immersed boundary methods
Immersed boundary (IB) methods have been successfully implemented for different applications. This paper focuses on the immersed boundary...
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An unfitted finite element method with direct extension stabilization for time-harmonic Maxwell problems on smooth domains
We propose an unfitted finite element method for numerically solving the time-harmonic Maxwell equations on a smooth domain. The embedded boundary of...
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High-Order CENO Finite-Volume Scheme with Anisotropic Adaptive Mesh Refinement: Efficient Inexact Newton Method for Steady Three-Dimensional Flows
A high-order finite-volume scheme with anisotropic adaptive mesh refinement (AMR) is combined with a parallel inexact Newton method for the solution...
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Active Flux Methods for Hyperbolic Systems Using the Method of Bicharacteristics
The Active Flux method is a third order accurate finite volume method for hyperbolic conservation laws, which is based on the use of point values as...
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Inverse Lax-Wendroff Boundary Treatment of Discontinuous Galerkin Method for 1D Conservation Laws
In this paper, we propose a new class of discontinuous Galerkin (DG) methods for solving 1D conservation laws on unfitted meshes. The standard DG...
