Finite volume element methods for nonequilibrium radiation diffusion equations

Zhao, Xiukun; Chen, Yanli; Gao, Yanni; Yu, Chunlei; Li, Yonghai

doi:10.1002/fld.3838

Cited by 18 publications

(19 citation statements)

References 27 publications

(41 reference statements)

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“…(28)- (29). We use the same idea as described in the previous section, that is, use some particular basis functions to get an interpolation approximation of E and B.…”

Section: Variable Substitution With B = Tmentioning

confidence: 98%

“…Yue and Yuan [28] designed a Picard-Newton iterative method with time-step control for multi-material non-equilibrium radiation diffusion problems. Zhao et al [29] constructed two finite volume element schemes, and proved that one of them is monotonic on distorted meshes and another is monotonic under some repairing techniques. Zhang et al [31] developed a discontinuous finite element method for 1D non-equilibrium radiation diffusion equations.…”

Section: Introductionmentioning

confidence: 99%

“…Many scientists devoted to study some efficient and accurate methods for solving the non-equilibrium radiation diffusion equations numerically [5,14,17,20,22,23,25,29,31]. Most of them focused on the nonlinear iteration technique and high-order time integrations.…”

Section: Introductionmentioning

confidence: 99%

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Monotone finite point method for non-equilibrium radiation diffusion equations

Huang

2015

Bit Numer Math

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In this paper, we propose the monotone tailored-finite-point method for solving the non-equilibrium radiation diffusion equations. We first give two tailored finite point schemes for the nonlinear parabolic equation in one-dimensional case, then extend the idea to solve the radiation diffusion problem in 1D as well as 2D. By using variable substitute, our method satisfies the discrete maximum principle automatically, thus preserves the properties of monotonicity and positivity. Numerical results show that our method can capture the sharp front and can be accommodated to discontinues diffusion coefficient.

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“…(28)- (29). We use the same idea as described in the previous section, that is, use some particular basis functions to get an interpolation approximation of E and B.…”

Section: Variable Substitution With B = Tmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

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Monotone finite point method for non-equilibrium radiation diffusion equations

Huang

2015

Bit Numer Math

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“…When the energy density E satisfies the relation E = T 4 , where T is temperature, the system is called in an equilibrium state and otherwise in a non-equilibrium state. Radiation diffusion has attracted considerable attention from researchers in the past; e.g., see [3,16,21,[23][24][25][28][29][30]. For example, foundations of radiation hydrodynamics can be found in the book [21] while numerical techniques for radiation diffusion and transport are addressed systematically in the book [3].…”

Section: Introductionmentioning

confidence: 99%

A moving mesh finite difference method for equilibrium radiation diffusion equations

Yang

Huang

Qiu

2015

Journal of Computational Physics

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An efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions. The method is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of meshing partial differential equations. The mesh adaptation is controlled through a Hessian-based monitor function and the so-called equidistribution and alignment principles. Several challenging issues in the numerical solution are addressed. Particularly, the radiation diffusion coefficient depends on the energy density highly nonlinearly. This nonlinearity is treated using a predictor-corrector and lagged diffusion strategy. Moreover, the nonnegativity of the energy density is maintained using a cutoff method which has been known in literature to retain the accuracy and convergence order of finite difference approximation for parabolic equations. Numerical examples with multimaterial, multiple spot concentration situations are presented. Numerical results show that the method works well for radiation diffusion equations and can produce numerical solutions of good accuracy. It is also shown that a two-level mesh movement strategy can significantly improve the efficiency of the computation.

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“…This difficulty has impeded the application of FVE methods on some complicated problems. Although there exist some works devoted to the application of FVE methods on complicated numerical simulations [14,37], these schemes are not monotone and the non-physical solutions are just modified by a simple cutoff method [21] or repair techniques [23]. To our best knowledge, few monotone FVE schemes have been found until now.…”

mentioning

confidence: 99%