Numerical Method of Modeling Thermal Creeping Flow in Heterogeneous Medium

The moving finite element method with streamline-upwind Petrov–Galerkin for magnetohydrodynamic flows problems at high Hartmann numbers

The \(hp\)-FEM is an adaptive version of the Finite Element Method (FEM) that is capable of achieving fast exponential convergence rates by combining optimally spatial refinements (\(h\)-adaptivity) with varying element polynomial degrees (\(p\)-adaptivity). We present a novel space-time adaptive \(hp\)-FEM algorithm that is capable of capturing accurately traveling sharp fronts in nonlinear time-dependent problems. The algorithm tries to assess the true approximation error directly (not via residuals or related techniques), and it does not involve any tuning parameters exposed to the user. The algorithm is compared to non-adaptive FEM as well as to adaptive FEM with low-order elements in the context of a model problem with moving sharp front that consists of two coupled nonlinear parabolic equations. Also the treatment of nonlinear terms is discussed and it is shown that replacing the Newton’s method with simpler linearizations can lead to considerable errors.

A LES model is proposed to predict the dispersion of particles in the atmosphere in the context of Chemical, Biological, Radiological and Nuclear (CBRN) applications. The code relies on the Finite Element Method (FEM) for both the fluid and the dispersed solid phases. Starting from the Navier-Stokes equations and a general description of the FEM strategy, the Streamline Upwind Petrov-Galerkin (SUPG) method is formulated putting some emphasis on the related assembly matrix and stabilization coefficients. Then, the Variational Multiscale Method (VMS) is presented together with a detailed illustration of its algorithm and hierarchy of computational steps. It is demonstrated that the VMS can be considered as a more general version of the SUPG method. The final part of the work is used to assess the reliability of the implemented predictor/multicorrector solution strategy.

A new continuous finite element SN method for solving first-order neutron transport equation

Vectorial finite element method for neutron transport solving with preconditioning GMRES acceleration

This paper examines the Streamline Upwind Petrov Galerkin method as a stabilizing technique for the numerical solution of differential equations of advection-diffusion-reaction; it analizes the method taking into account the non self-adjoint nature of the convective diferential operator and the necessary transformations for the solution stabilization through the elimination of non self-adjoint effect induced by the convective term. Presents six different numerical examples, which include problems of variable coefficients, high convective problems, highly reactive systems and transitional solutions. This method presents an excellent performance of this stabilization technique for all the cases mentioned above, except for the problems with strong reactives terms.

A nonlinear filtering algorithm for multi-dimensional finite element pollutant advection schemes

We present implicit time integration schemes suitable for modeling free surface Stokes flow dynamics with marker in cell (MIC) based spatial discretization. Our target is for example thermal convection surrounded by deformable surface boundaries to simulate the long term planetary formation process. The numerical system becomes stiff when the dynamical balancing time scale for the increasing/decreasing load by surface deformation is very short compared with the time scale associated with thermal convection. Any explicit time integration scheme will require very small time steps; otherwise, serious numerical oscillation (spurious solutions) will occur. The implicit time integration scheme possesses a wider stability region than the explicit method; therefore, it is suitable for stiff problems. To investigate an efficient solution method for the stiff Stokes flow system, we apply first (backward Euler (BE)) and second order (trapezoidal method (TR) and trapezoidal rule—backward difference formula (TR-BDF2)) accurate implicit methods for the MIC solution scheme. The introduction of implicit time integration schemes results in nonlinear systems of equations. We utilize a Jacobian free Newton Krylov (JFNK) based Newton framework to solve the resulting nonlinear equations. In this work we also investigate two efficient implicit solution strategies to reduce the computational cost when solving stiff nonlinear systems. The two methods differ in how the advective term in the material transport evolution equation is treated. We refer to the method that employs Lagrangian update as “fully implicit” (Imp), whilst the method that employs Eulerian update is referred to as “semi-implicit” (SImp). Using a finite difference (FD) method, we have performed a series of numerical experiments which clarify the accuracy of solutions and trade-off between the computational cost associated with the nonlinear solver and time step size. In comparison with the general explicit Euler method, the second order accurate Imp methods reduce total computational cost successfully through the utilization of a large time step without sacrificing accuracy and stability. Moreover, the proposed SImp method is effective in reducing the computational cost associated with evaluating the nonlinear residual while obtaining a solution similar to the Imp method.

In this paper an analysis is carried out to study the efficiency of heat distribution through fins using finite element method (FEM) and differential quadrature method ( DQM). Numerical solutions are obtained using both methods for temperature distribution over the fin surface. Analysis of surface solutions in terms of temperature and error distributions have been presented here. Solutions are also obtained using equally spaced (conventional) and non-equally spaced (optimum) mesh (nodal points) distribution techniques. Two-dimensional heat conduction problem has been solved in both equal and non-equal nodal points distribution cases (called here conventional FEM (CFEM) and conventional DQM (CDQM) and optimum FEM (OFEM) and optimum DQM (ODQM)). The obtained results are compared and investigated with exact results. The best results are found in OFEM solutions. It is also found that, ODQM solutions reach very close to OFEM solutions with negligible error, whereas CFEM and CDQM solutions diverges with increasing number of nodal(mesh) points.

Comparison of Eulerian and Lagrangian numerical techniques for the Stokes equations in the presence of strongly varying viscosity

In recent years Line Start Permanent Magnet (LSPM) motor has attracted a lot of attention thanks to many advantages, such as high efficiency, high power factor, and high power density. In this motor, at the start, the risk of irreversible demagnetization in Permanent Magnet (PM) is essential due to the large inrush current. So in this paper using Finite Element Method (FEM) the effective factors on demagnetization of this motor structure at various temperatures will be investigated. In addition, the sensitivity analysis will be carried out. Finally, the electromagnetic torque of this motor using a modified FEM algorithm will be calculated and compared to the conventional FEM algorithm.

Simulation of hyperelastic materials in real-time using deep learning.

Analysis and application of an overlapped FEM-BEM for wave propagation in unbounded and heterogeneous media

On the relation of the Embedded Discontinuous Galerkin method to the stabilized residual-based finite element methods

Extending FEniCS to work in higher dimensions using tensor product finite elements