Transient Rayleigh-Bénard Thermal Convection With Radiation Heat Transfer in Participating Media Using the Control Volume Finite Element Method (CVFEM) and Lattice Boltzmann Method

In this paper, a gas-kinetic Bhatnagar-Gross-Krook (BGK) model is constructed for the Rayleigh-Benard thermal convection transfer in a two-dimensional cavity containing an absorbing, emitting, and scattering medium, where the flow field and temperature field are described by two coupled Lattice Boltzmann Method (LBM) BGK models. Heat radiation is solved using the Control Volume Finite Element Method (CVFEM). The two-dimensional Rayleigh-Benard thermal convection with radiation is studied and numerical results are compared with some available benchmark solutions and a good agreement has been observed.

Simulating the behaviour of Glioblastoma Multiforme based on patient MRI during treatments

Glioblastoma Multiforme is a brain cancer that still show poor prognosis for patients despite the active researches for new treatments. In this work the goal is to model and simulate the evolution of tumour associated angiogenesis and the therapeutic response of the Glioblastoma Multiforme. Multiple phenomena are modelled in order to fit different biological pathways, such as, the cellular cycle, apoptosis, hypoxia or angiogenesis.This results in a nonlinear system with 4 equations and 4 unknowns: the density of tumour cells, the $O_{2}$ concentration, the density of endothelial cells and the vascular endothelial growth factor concentration.This system is solved numerically on a 2D-slice of Magnetic Resonance Imaging, using a nonlinear control volume finite element scheme on a mesh fitting the geometry of the brain and the tumour of a patient.We show that this implicit volume finite element numerical scheme is positive and we give energy estimates on the discrete solution to ensure convergence.The numerical scheme is implicit in time.Numerical simulations of this scheme have been done using the different standard treatments: surgery, chemotherapy and radiotherapy, in order to understand the behaviour of tumour in response to treatments.

A Second-Order Stabilized Control Volume Finite Element Method for Self-Heating Effects Simulation of Semiconductor Devices based on Triangular Elements

A second-order control volume finite element method combined with the multiscale flux approximation (CVFEM-MS) based on triangular elements is proposed to numerically investigate the self-heating effects of semiconductor devices. The multiscale fluxes are combined with a selected set of second-order vector basis functions to stabilize the discretization of carrier continuity equations with respect to triangular elements. Numerical results reveal that the proposed method is robust and accurate, even on the mesh of low-quality, where the detrimental impacts caused by the severe self-heating on the terminal currents can be obviously observed for a bipolar transistor model.

Improved Control Volume Method for Thermoelastic Analysis of Functionally Graded Solids

In this work, an improved control volume finite element method (ICVFEM) is proposed and implemented for thermoelastic analysis in functionally graded materials (FGMs) at steady state. Different from the conventional CVFEM, the sub-control volume used in the proposed method is a circular in the intrinsic coordinate. The advantages of the new integral domain are: (i) the complex integration path can be avoided, (ii) the method is very suitable for many types of elements. High-order shape functions of eight quadrilateral (Q8) elements are used to obtain the unknown variables and their derivatives. Besides, material properties in a functionally graded structure are calculated by the high-order shape functions based on the properties defined at the node. To verify the convergence and accuracy of the proposed method, three numerical examples with analytical solutions are illustrated by using the conventional CVFEM and FEM at the same time.

Monitoring and modeling of part thickness evolution in vacuum infusion process

The main hurdles in Vacuum Infusion (VI) are the difficulty in achieving complete mold filling and uniform part thickness. This study integrates process monitoring by full field thickness measurements and resin flow modeling that accounts for compaction and permeability characterizations of fabric reinforcements to assess the evolution of part thickness during filling and post-filling stages of VI process. A Structured Light Scanning system is used for full field thickness monitoring in experiments and a Control Volume Finite Element Method solver is implemented to couple resin flow with fabric’s compaction and permeability. Two cases are studied both experimentally and numerically. Evolutions of thickness and pressure validate the developed flow solver, its accuracy in terms of predicting fill times and fill patterns, suitability and limitations of the elastic compaction models for thickness modeling.

On the Performance of the Node Control Volume Finite Element Method for Modeling Multi-phase Fluid Flow in Heterogeneous Porous Media

In this paper, we critique the performance of the node control volume finite element (NCVFE) method for modeling multi-phase fluid flow in heterogeneous media. The NCVFE method solves for the pressure at the vertices of elements and a control volume mesh is constructed around them. Material properties are defined on elements, while transport is simulated on the control volumes. These two meshes are not aligned producing inaccurate results and artificial fluid smearing when modeling multi-phase fluid flow in heterogeneous media. We perform numerical tests to quantify and visualize the extent of this artificial fluid smearing in domains with different material properties. The domains are composed of tetrahedron finite elements. Large artificial fluid smearing is observed in coarse meshes; however, it decreases with the increase in mesh resolution. These findings prompt the use of high-resolution meshes for the method and the need for development of novel numerical methods to address this unphysical flow.

Enhanced positive vertex-centered finite volume scheme for anisotropic convection-diffusion equations

This article is about the development and the analysis of an enhanced positive control volume finite element scheme for degenerate convection-diffusion type problems. The proposed scheme involves only vertex unknowns and features anisotropic fields. The novelty of the approach is to devise a reliable upwind approximation with respect to flux-like functions for the elliptic term. Then, it is shown that the discrete solution remains nonnegative. Under general assumptions on the data and the mesh, the convergence of the numerical scheme is established owing to a recent compactness argument. The efficiency and stability of the methodology are numerically illustrated for different anisotropic ratios and nonlinearities.