Smoothed particle hydrodynamics is a completely mesh-free method to simulate fluid flow. Rather than representing the physical variables on a fixed grid, the fluid is represented by freely moving interpolation centers (”particles”). Apart from their position and velocity these particles carry information about the physical quantities of the considered fluid, such as temperature, composition, ch...

The development of smoothed projections, constructed by combining the canonical interpolation operators defined from the degrees of freedom with a smoothing operator, has proved to be an effective tool in finite element exterior calculus. The advantage of these operators is that they are L2 bounded projections, and still they commute with the exterior derivative. In the present paper we general...

A finite element method with an adaptive mesh redistribution technique is presented for solving the Kohn-Sham equation. The mesh redistribution strategy is based on the harmonic mapping, and the movement of grid points is partially controlled by the monitor function that depends on the gradient of the electron density. Compared with fixed meshes, both efficiency and accuracy of the solution are...

Nowadays, events like severe earthquakes or man-made malicious actions are often taken into account in structural design of critical infrastructures and consequently high dynamic loads are considered in structural analyses. In particular, it is aimed to reproduce large displacements fields, dynamic fracture mechanisms (fragmentations, etc.) and high stress concentrations. Classical numerical me...

The Finite Element Method (FEM) has become the standard tool for the analysis of a wide range of mechanical problems. However, the classical FEM is not well suited for the treatment of large deformation problems since excessive mesh distortions require remeshing. The Material Point Method (MPM) represents an approach in which material points moving through a fixed finite element grid are used t...

Nowadays, events like severe earthquakes or man-made malicious actions are often taken into account in structural design of critical infrastructures and consequently high dynamic loads are considered in structural analyses. Classical numerical methods, like Finite Element Method (FEM), may be inadequate to model the mechanical behavior of structural elements under such actions. In fact high def...

n this work, computational fluid dynamics of the flow behavior in a cold flow of fluidized bed is studied. An improved finite volume based finite element method has been introduced to solve the two-phase gas/solid flow hydrodynamic equations. This method uses a collocated grid, where all variables are located at the nodal points. The fluid dynamic model for gas/solid two-phase flow is based on ...

In this paper, we analyze a scheme for the time-dependent variable density Navier-Stokes equations. The algorithm is implicit in time, and the space approximation is based on a low-order staggered non-conforming finite element, the so-called Rannacher-Turek element. The convection term in the momentum balance equation is discretized by a finite volume technique, in such a way that a solution ob...

We introduce the coarsening of finite element computational grid strategy into the method proposed by Kačur and Mikula in [11] for the numerical solution of the Perona–Malik model modified in the sense of Catté, Lions, Morel and Coll. It improves the efficiency of the method, while the solution tends to be more flat during the selective smoothing process applied to the image. The numerical appr...