We consider solving a generalized Allen-Cahn equation coupled with passive convection for given incompressible velocity field. The numerical scheme consists of the first order accurate stabilized implicit explicit time discretization and fourth finite difference scheme, which is obtained from formulation $Q^2$ spectral element method. prove that discrete maximum principle holds under suitable m...

In this letter, we present a computational framework based on the use of the Newton and level set methods and tailored for the modeling of bubbles with surface tension in a surrounding Newtonian fluid. We describe a fully implicit and monolithic finite element method that maintains stability for significantly larger time steps compared to the usual explicit method and features substantial compu...

Discrete particle simulations are widely used to study large–scale particulate flows in complex geometries where particle–particle and particle–fluid interactions require an adequate representation but the computational cost has to be kept low. In this work, we present a novel coupling approach for such simulations. A lattice Boltzmann formulation of the generalized Navier–Stokes equations is u...

We derive in this paper a unified framework for a priori and a posteriori error analysis of mixed finite element discretizations of second-order elliptic problems. It is based on the classical primal weak formulation, the postprocessing of the potential proposed in [T. Arbogast and Z. Chen, On the implementation of mixed methods as nonconforming methods for secondorder elliptic problems, Math. ...

Currently in most global meteorological applications, the spectral transform method or low-order finite difference/finite element methods are used. The spectral transform method, which yields high-order approximations, requires Legendre transforms. The Legendre transforms have a computational complexity of O(N3), where N is the number of subintervals in one dimension, and thus render the spectr...

Extrapolation methods for the solution of partial diierentialequations are commonly based on the existence of error expansions for the approximate solution. Implicit extrapolation, in the contrast, is based on applying extrapolation indirectly, by using it on quantities like the residual. In the context of multigrid methods, a special technique of this type is known as-extrapolation. For nite e...

A numerical modelling approach capable of simulating Shot Peening (SP) processes of industrial interest was developed by combining the Discrete Element Method (DEM) with the Finite Element Method (FEM). In this approach, shot-shot and shot-target interactions as well as the overall shot flow were simulated efficiently using rigid body dynamics. A new algorithm to dynamically adapt the coefficie...

in the present study, a spectral finite element method is developed for free and forced transverse vibration of levy-type moderately thick rectangular orthotropic plates based on first-order shear deformation theory. levy solution assumption was used to convert the two-dimensional problem into a one-dimensional problem. in the first step, the governing out-of-plane differential equations are tr...