Meshfree methods for nonlinear equilibrium radiation diffusion equation with jump coefficient. (English) Zbl 1538.65421
Summary: The equilibrium radiation diffusion equation has been widely used in astrophysics, inertial confinement fusion and others. Since the simulation domain consists of many complicated domains and the material properties in each domain are different, the diffusion coefficient usually has a strong discontinuity at the interface. Because the equilibrium radiation diffusion equation is often built on complicated domains as well as interfaces and has a strong nonlinearity, it is challenging to solve by means of finite difference method and so on. By treating \(T^4\) with different linearization methods, three meshfree methods are utilized to approximate the two-dimensional equilibrium radiation diffusion equation with jump coefficient. Firstly, the time term is discretized by the fully implicit scheme. Then, three different linearization methods (direct linearization, Picard-Newton linearization and Richtmyer linearization) are utilized to linearize \(T^4\). Finally, the linearized algebraic equations are solved numerically by a non-symmetric collocation method with a compactly supported radial basis function. Numerical experiments are performed on the three algorithms for different regular and irregular domains with highly curved interfaces. The effectiveness of the proposed algorithms is verified by numerical results.
MSC:
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65N35 | Spectral, collocation and related methods for boundary value problems involving PDEs |
| 65H10 | Numerical computation of solutions to systems of equations |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65D17 | Computer-aided design (modeling of curves and surfaces) |
| 80A21 | Radiative heat transfer |
| 35K35 | Initial-boundary value problems for higher-order parabolic equations |
Keywords:
jump coefficient; radiation diffusion equation; meshfree methods; radial basis function; fully implicit discretizationSoftware:
MatlabReferences:
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