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We introduce a new abstraction for the representation and solution of multi-domain problems using finite element methods. This is an advance over previous work in that it achieves a single higher-level abstraction that represents…

The goal of this report is to present the final project conducted in order to fulfill the requirements of the M.Sc. degree at the Department of Mechanical Engineering, Ben-Gurion University (BGU) of the Negev. The project comprises…

Non-orthogonality errors in unstructured Finite Volume methods for simulating incompressible two-phase flows may break the force-balanced discretization. We show that applying the same explicit non-orthogonality correction for all gradient…

Mortar methods are widely used techniques for discretizations of partial differential equations and preconditioners for the algebraic systems resulting from the discretizations. For problems with high contrast and multiple scales, the…

In this work, we introduce new second-order schemes for one- and two-dimensional hyperbolic systems of conservation laws. Following an approach recently proposed in [{\sc R. Abgrall}, Commun. Appl. Math. Comput., 5 (2023), pp. 370--402], we…

We describe an exact and highly efficient numerical algorithm for solving a special but important class of convection-diffusion equations. These equations occur in many problems in physics, chemistry, or biology, and they are usually hard…

The diffuse medium in and around galaxies can exist in a multi-phase state: small, cold gas clouds contributing significantly to the total mass embedded in pressure equilibrium with a hotter, more diffuse volume-filling component. Modeling…

A semi-Lagrangian method for parabolic problems is proposed, that extends previous work by the authors to achieve a fully conservative, flux-form discretization of linear and nonlinear diffusion equations. A basic consistency and…

We consider numerical algorithms for the simulation of the rheology of two-dimensional vesicles suspended in a viscous Stokesian fluid. The vesicle evolution dynamics is governed by hydrodynamic and elastic forces. The elastic forces are…

Coupled nonlinear system of reaction-diffusion equations describing multi-component (species) interactions with heterogeneous coefficients is considered. Finite volume method based approximation for the space is used to construct…

We propose a novel early-terminating mesh refinement strategy using an integrated residual method to solve dynamic feasibility problems. As a generalization of direct collocation, the integrated residual method is used to approximate an…

This dissertation resolves a longstanding discussion of a mathematical problem important in contaminant hydrogeology and chemical-reaction engineering, the proper mathematical description for a miscible solute undergoing longitudinal…

Centered finite volume methods are considered in the context of Numerical Relativity. A specific formulation is presented, in which third-order space accuracy is reached by using a piecewise-linear reconstruction. This formulation can be…

In this paper, we investigate the application of the maximum principle preserving (MPP) parametrized flux limiters to the high order finite volume scheme with Runge-Kutta time discretization for solving convection dominated problems. Such…

Flocculation is the process whereby particles (i.e., flocs) in suspension reversibly combine and separate. The process is widespread in soft matter and aerosol physics as well as environmental science and engineering. We consider a general…

A number of different multiscale methods have been developed as a robust alternative to upscaling and as a means for accelerated reservoir simulation of high-resolution geomodels. In their basic setup, multiscale methods use a restriction…

We propose certain approach of solving two-dimensional non-stationary and stationary advection-diffusion-reaction boundary value problems through their reduction to the set of corresponding one-dimensional problems. This method leverages…

Accretion disks are three-dimensional, turbulent, often self-gravitating, magnetohydrodynamic flows, which can be modeled in detail with numerical simulations. In this paper, we present a new algorithm that is based on a spectral…

A new discretization approach is presented for the simulation of flow in complex poro-fractured media described by means of the Discrete Fracture and Matrix Model. The method is based on the numerical optimization of a properly defined…

In this work we study the dynamic behaviour of compound shells of revolution partially filled with an ideal incompressible fluid based on boundary-value problems. New analytical mathematical model with corresponding discrete scheme for the…