Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
SIAM Journal on Numerical Analysis
Immersed Interface Methods for Stokes Flow with Elastic Boundaries or Surface Tension
SIAM Journal on Scientific Computing
Wave propagation algorithms for multidimensional hyperbolic systems
Journal of Computational Physics
Fictitious domain method for unsteady problems: application to electromagnetic scattering
Journal of Computational Physics
SIAM Journal on Numerical Analysis
A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method)
Journal of Computational Physics
A Cartesian grid finite-volume method for the advection-diffusion equation in irregular geometries
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Journal of Computational Physics
The immersed interface method for the Navier-Stokes equations with singular forces
Journal of Computational Physics
How to Incorporate the Spring-Mass Conditions in Finite-Difference Schemes
SIAM Journal on Scientific Computing
An Immersed Interface Method for Incompressible Navier-Stokes Equations
SIAM Journal on Scientific Computing
Comparison of Taylor finite difference and window finite difference and their application in FDTD
Journal of Computational and Applied Mathematics
Review: Dynamic analysis of fluid-soil-structure interaction problems by the boundary element method
Journal of Computational Physics
δ-mapping algorithm coupled with WENO reconstruction for nonlinear elasticity in heterogeneous media
Applied Numerical Mathematics
Journal of Computational Physics
Journal of Computational Physics
Effective stretching strategies for paraxial lightwave propagation simulations
Computers and Structures
Journal of Computational Physics
High-performance modeling acoustic and elastic waves using the parallel Dichotomy Algorithm
Journal of Computational Physics
Numerical modeling of transient two-dimensional viscoelastic waves
Journal of Computational Physics
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We present a numerical method to take into account 2D arbitrary-shaped interfaces in classical finite-difference schemes, on a uniform Cartesian grid. This work extends the "explicit simplified interface method" (ESIM), previously proposed in 1D [J. Comput. Phys. 168 (2001) 227-248]. The physical problem under study concerns the linear hyperbolic systems of acoustics and elastodynamics, with stationary interfaces. Our method maintains, near the interfaces, properties of the schemes in homogeneous medium, such as the order of accuracy and the stability limit. Moreover, it enforces the numerical solution to satisfy the exact interface conditions. Lastly, it provides subcell geometrical features of the interface inside the meshing. The ESIM can be coupled automatically with a wide class of numerical schemes (Lax-Wendroff, flux-limiter schemes, etc.) for a negligible additional computational cost. Throughout the paper, we focus on the challenging case of an interface between a fluid and an elastic solid. In numerical experiments, we provide comparisons between numerical solutions and original analytic solutions, showing the efficiency of the method.