Related papers: Finite-difference methods for simulation models in…
A comprehensive scheme for the spatial discretisation of continuity equation, momentum advection and normal and shear stresses at the fluid interfaces is presented for numerically simulating the incompressible two phase flows based on the…
This paper studies formulations of second-order elliptic partial differential equations in nondivergence form on convex domains as equivalent variational problems. The first formulation is that of Smears \& S\"uli [SIAM J.\ Numer.\ Anal.\…
A computational tool for coarse-graining nonlinear systems of ordinary differential equations in time is discussed. Three illustrative model examples are worked out that demonstrate the range of capability of the method. This includes the…
Deformable elastic bodies in viscous and viscoelastic media constitute a large portion of synthetic and biological complex fluids. We present a parallelized 3D-simulation methodology which fully resolves the momentum balance in the solid…
We present an immersed boundary method to simulate the creeping motion of a rigid particle in a fluid described by the Stokes equations discretized thanks to a finite element strategy on unfitted meshes, called Phi-FEM, that uses the…
In this paper the numerical approximation of solutions of Liouville-Master Equations for time-dependent distribution functions of Piecewise Deterministic Processes with memory is considered. These equations are linear hyperbolic PDEs with…
We discuss alternative iteration methods for differential equations. We provide a convergence proof for exactly solvable examples and show more convenient formulas for nontrivial problems.
This study concerns with singularly perturbed systems of second-order reaction-diffusion equations in ODE's. To handle this type of problems, a numerical-asymptotic hybrid method is employed. In this hybrid method, an efficient asymptotic…
This paper presents a new resolution strategy for multi-scale streamer discharge simulations based on a second order time adaptive integration and space adaptive multiresolution. A classical fluid model is used to describe plasma…
In this paper, we propose a multiphysics finite element method for a nonlinear poroelasticity model. To better describe the processes of deformation and diffusion, we firstly reformulate the nonlinear fluid-solid coupling problem into a…
Currently existing energy-stable parametric finite element methods for surface diffusion flow and other flows are usually limited to first-order accuracy in time. Designing a high-order algorithm for geometric flows that can also be…
Particle methods are less computationally efficient than grid based numerical solution of the Navier Stokes equation. However, they have important advantages including rigorous mass conservation, momentum conservation and isotropy. In…
The numerical methods for differential equation solution allow obtaining a discrete field that converges towards the solution if the method is applied to the correct problem. Nevertheless, the numerical methods have the restricted class of…
We develop a fully discrete scheme for time-fractional diffusion equations by using a finite difference method in time and a finite element method in space. The fractional derivatives are used in Caputo sense. Stability and error estimates…
This papers deals with a construction and convergence analysis of a finite difference scheme for solving time-fractional porous medium equation. The governing equation exhibits both nonlocal and nonlinear behaviour making the numerical…
We present an algorithm for the numerical solution of the equations governing combustion in porous inert media. The discretization of the flow problem is performed by the mixed finite element method, the transport problems are discretized…
The diffusive viscous wave equation describes wave propagation in diffusive and viscous media. Examples include seismic waves traveling through the Earth's crust, taking into account of both the elastic properties of rocks and the…
In the present chapter we focus on the fundamentals of non-grid-conforming numerical approaches to simulating particulate flows, implementation issues and grid convergence vs. available reference data. The main idea is to avoid adapting the…
Two finite volume methods are derived and applied to the solution of problems of incompressible flow. In particular, external inviscid flows and boundary-layer flows are examined. The firstmethod analyzed is a cell-centered finite volume…
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…