A Raviart-Thomas mixed finite element scheme for the two-dimensional three-temperature heat conduction problems

Abstract

Summary For the two‐dimensional three‐temperature radiative heat conduction problem appearing in the inertial confinement numerical stimulations, we choose the Freezing coefficient method to linearize the nonlinear equations, and initially apply the well‐known mixed finite element scheme with the lowest order Raviart–Thomas element associated with the triangulation to the linearized equations, and obtain the convergence with one order with respect to the space direction for the temperature and flux function approximations, and design a simple but efficient algorithm for the discrete system. Three numerical examples are displayed. The former two verify theoretical results and show the super‐convergence for temperature and flux functions at the barycenter of the element, which is helpful for solving the radiative heat conduction problems. The third validates the robustness of this scheme with small energy conservative error and one order convergence for the time discretization. Copyright © 2016 John Wiley & Sons, Ltd.

A Vertex-Centered and Positivity-Preserving Finite Volume Scheme for Two-Dimensional Three-Temperature Radiation Diffusion Equations on General Polygonal Meshes

“…As a result, (2.1a)-(2.3) becomes a closed and well-posed system [31,33]. This system approximately describes the process of radiant energy spreading in the quiescent medium and energy exchange of electrons with photons and ions.…”

“…In [7], two finite volume element schemes were constructed on triangular meshes. The authors in [31] adopted the freezing coefficient method to linearize the nonlinear equations and then solved the resulting equations by Raviart-Thomas mixed finite element method.…”

“…The first and fifth features are the main differences from the ones in [9], while the rest ones make it most attractive than those in [7,31,51]. The rest of this paper is organized as follows.…”

An extremum‐preserving finite volume scheme for three‐temperature radiation diffusion equations

“…In An et al, 8 an improved Anderson acceleration method is proposed to accelerate the convergence of nonlinear iteration. By applying the lowest order Raviart-Thomas element for spatial discretization, a mixed finite element scheme 10 is constructed to solve the 2D 3-T radiation diffusion equations. In previous studies, [11][12][13][14] several new parallel adaptive numerical methods are presented to further study the equations.…”

Boundary Element Mathematical Modelling and Boundary Element Numerical Techniques for Optimization of Micropolar Thermoviscoelastic Problems in Solid Deformable Bodies

“…Then, Eringen [25] and Nowacki [26] extended it to micropolar thermoelasticity, and then implemented in various applications [27][28][29]. Because of strong nonlinearity of three-temperatures radiative heat conduction equations, the numerical solution and simulation of such problems are always difficult and require the development of new numerical schemes [30,31]. In comparison with other numerical methods [32][33][34], the boundary element method has been successfully applied and performed for solving various applications .…”