Related papers: A simple numerical method for Hele-Shaw type probl…
We present a new composite mesh finite element method for fluid--structure interaction problems. The method is based on surrounding the structure by a boundary-fitted fluid mesh which is embedded into a fixed background fluid mesh. The…
Solutions to optimal control problems can be discontinuous, even if all the functionals defining the problem are smooth. This can cause difficulties when numerically computing solutions to these problems. While conventional numerical…
We consider the homogenization of the Hele-Shaw problem in periodic media that are inhomogeneous both in space and time. After extending the theory of viscosity solutions into this context, we show that the solutions of the inhomogeneous…
We present a numerical method for approximating the solutions of degenerate parabolic equations with a formal gradient flow structure. The numerical method we propose preserves at the discrete level the formal gradient flow structure,…
We study a Hele-Shaw problem with a mushy region obtained as a Mesa type limit of one phase Stefan problems in exterior domains. We study the convergence, determine some of the qualitative properties and regularity of the unique limiting…
The accurate representation of surface tension driven flows in multiphase systems is considered a challenging problem to resolve numerically. Although there have been extensive works in the past that have presented approaches to resolve…
This paper presents an efficient spectral method for solving the fractional Fredholm integro-differential equations. The non-smoothness of the solutions to such problems leads to the performance of spectral methods based on the classical…
Numerical issues arising in computations of viscous flows in corners formed by a liquid-fluid free surface and a solid boundary are considered. It is shown that on the solid a Dirichlet boundary condition, which removes multivaluedness of…
The results from a series of well characterised, unstable, miscible displacement experiments in a Hele Shaw cell with a quarter five-spot source-sink geometry are presented, with comparisons to detailed numerical simulation. We perform…
When solving partial differential equations using classical schemes such as finite difference or finite volume methods, sufficiently fine meshes and carefully designed schemes are required to achieve high-order accuracy of numerical…
This paper presents an adaptive numerical framework for solving exterior "sound-soft" scattering problems governed by the Helmholtz equation. By interpreting the Method of Fundamental Solutions through the lens of rational approximation, we…
Free boundary problems deal with systems of partial differential equations, where the domain boundaries are apriori unknown. Due to this special characteristic, it is challenging to solve free boundary problems either theoretically or…
In this paper, we develop a numerical method for the computation of (quasi-)resonances in spherical symmetric, heterogeneous Helmholtz problems with piecewise smooth refractive index. Our focus lies in resonances very close to the real…
In this paper, we describe a numerical method to solve numerically the weakly dispersive fully nonlinear Serre-Green-Naghdi (SGN) celebrated model. Namely, our scheme is based on reliable finite volume methods, proven to be very effective…
A high-frequency recovered fully discrete low-regularity integrator is constructed to approximate rough and possibly discontinuous solutions of the semilinear wave equation. The proposed method, with high-frequency recovery techniques, can…
This paper presents a high-accuracy higher-order multiscale method for solving multi-continuum problems in in highly heterogeneous media. First, microscopic unit cell functions are defined, leading to the derivation of macroscopic…
In this paper, we propose a method of fundamental solutions for the problems of two-dimensional potential flow past a doubly-periodic array of obstacles. The solutions of these problems involve doubly-periodic functions, and it is difficult…
Topology changes in multi-phase fluid flows are difficult to model within a traditional sharp interface theory. Diffuse interface models turn out to be an attractive alternative to model two-phase flows. Based on a…
We investigate a generalized Hele-Shaw equation with a source and drift terms where the density is constrained by an upper-bound density constraint that varies in space and time. By using a generalized porous medium equation approximation,…
Waves scattering from unbounded structures are always complicated problems for numerical simulations. For the case that the non-periodic incident field scattered by (locally perturbed) periodic surfaces, with the help of the Bloch…