Related papers: A method of fundamental solutions for doubly-perio…
In undergraduate classes, the potential flow that goes around a circular cylinder is designed for complemental understanding of mathematical technique to handle the Laplace equation with Neumann boundary conditions and the physical concept…
We develop an embedded boundary method (EBM) to solve the two-phase incompressible flow with piecewise constant density. The front tracking method is used to track the interface. The fractional step methods are used to solve the…
There are several methods for proving the existence of the solution to the elliptic boundary problem $Lu=f \text{\,\, in\,\,} D,\quad u|_S=0,\quad (*)$. Here $L$ is an elliptic operator of second order, $f$ is a given function, and…
In this paper, we present a multiscale method for simulations of the multicontinua unsaturated flow problems in heterogeneous fractured porous media. The mathematical model is described by the system of Richards equations for each continuum…
The double-layer potential plays an important role in solving boundary value problems for elliptic equations, and in the study of which for a certain equation, the properties of the fundamental solutions of the given equation are used. All…
We present a new direct simulation Monte-Carlo method for solving the relativistic Boltzmann equation. We solve numerically the 2-dimensional Boltzmann equation using this new algorithm. We find that elliptic flow from this transport…
We study a thermodynamically consistent diffuse-interface model that describes the motion of two macroscopically immiscible, incompressible, and viscous Newtonian fluids with unmatched densities. This model is compatible with continuum…
The quasi-geostrophic two-layer (QS2L) system models the dynamic evolution of two interconnected potential vorticities, each is governed by an active scalar equation. These vorticities are linked through a distinctive combination of their…
We prove existence of strong solutions to a family of some semilinear parabolic free boundary problems by means of elliptic regularization. Existence of solutions is obtained in two steps: we first show some uniform energy estimates and…
In this paper, we discuss a general approach to find periodic solutions bifurcating from equilibrium points of classical Vlasov systems. The main access to the problem is chosen through the Hamiltonian representation of any Vlasov system,…
We use the vorticity transportation equation as the start point--with the help of stream function for two-dimensional planar incompressible flows--to obtain exact solutions that characterize evolution and dynamics of the flows. These…
We consider a thermodynamically consistent diffuse interface model describing two-phase flows of incompressible fluids in a non-isothermal setting. This model was recently introduced in a previous paper of ours, where we proved existence of…
As groundwater is an essential nutrition and irrigation resource, its pollution may lead to catastrophic consequences. Therefore, accurate modeling of the pollution of the soil and groundwater aquifer is highly important. As a model, we…
A two-level overlapping Schwarz method is developed for second order elliptic problems with highly oscillatory and high contrast coefficients, for which it is known that the standard coarse problem fails to give a robust preconditioner. In…
A new analytical criterion that captures the onset of separation of flow past elliptic cylinders is derived by considering the variation of the wall normal velocity in Reynolds number parameter space. It is shown that this criterion can be…
Wave propagation and acoustic scattering problems require vast computational resources to be solved accurately at high frequencies. Asymptotic methods can make this cost potentially frequency independent by explicitly extracting the…
In this work, we establish a continuous version of the Fountain theorem by using the framework of the weak slope for continuous functionals, which generalizes Theorem 3.6 of Willem \cite{Wi}. Then we present an application to a semilinear…
In this paper a new primal-dual mixed finite element method is introduced, aimed to model multiscale problems with several geometric subregions in the domain of interest. In each of these regions porous media fluid flow takes place, but…
Using continuation methods, we study the global solution structure of periodic solutions for a class of periodically forced equations, generalizing the case of relativistic pendulum. We obtain results on the existence and multiplicity of…
In this paper we treat the numerical approximation of the two-phase parabolic obstacle-like problem: \[\Delta u -u_t=\lambda^+\cdot\chi_{\{u>0\}}-\lambda^-\cdot\chi_{\{u<0\}},\quad (t,x)\in (0,T)\times\Omega,\] where $T < \infty, \lambda^+…