What is it about?
We provide a well-behaved fully implicit nonlinear scheme for nonlinear convection diffusion equation to capture the transient feature of the problem, and design Picard–Newton iteration with a quadratic convergent ratio to realize fast solution. Also we illustrate some fundamental properties of the nonlinear scheme and iteration such as the convergence accuracy and speed.
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Why is it important?
By proposing the fully implicit schemes and iterations, we acquire accurate and efficient simulation of the convection diffusion problem. By developing new induction hypothesis reasoning, we overcome the difficulty caused by the conservative diffusion operator, and rigorously analyze their properties to assure the credibility of the methods. The reasoning method here differs from those for linearization schemes and is applicable to other nonlinear problems.
Perspectives
The numerical method provides theoretical and technical support to accelerate resolving convection diffusion, non-equilibrium radiation diffusion and radiation transport problems. The induction hypothesis reasoning method can be applied to other fully implicit discrete schemes for other nonlinear problems.
Xia Cui
Institute of Applied Physics and Computational Mathematics, Beijing, China
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This page is a summary of: An efficient solving method for nonlinear convection diffusion equation, International Journal of Numerical Methods for Heat & Fluid Flow, January 2018, Emerald,
DOI: 10.1108/hff-10-2016-0403.
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