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首页> 外文期刊>International journal of numerical methods for heat & fluid flow >An efficient solving method for nonlinear convection diffusion equation
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An efficient solving method for nonlinear convection diffusion equation

机译：非线性对流扩散方程的一种有效求解方法。

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摘要

Purpose - This paper aims to provide a well-behaved nonlinear scheme and accelerating iteration for the nonlinear convection diffusion equation with fundamental properties illustrated. Design/methodology/approach - A nonlinear finite difference scheme is studied with fully implicit (FI) discretization used to acquire accurate simulation. A Picard-Newton (PN) iteration with a quadratic convergent ratio is designed to realize fast solution. Theoretical analysis is performed using the discrete function analysis technique. By adopting a novel induction hypothesis reasoning technique, the L~∞ (H~I) convergence of the scheme is proved despite the difficulty because of the combination of conservative diffusion and convection operator. Other properties are established consequently. Furthermore, the algorithm is extended from first-order temporal accuracy to second-order temporal accuracy. Findings - Theoretical analysis shows that each of the two FI schemes is stable, its solution exists uniquely and has second-order spatial and first/second-order temporal accuracy. The corresponding PN iteration has the same order of accuracy and quadratic convergent speed. Numerical tests verify the conclusions and demonstrate the high accuracy and efficiency of the algorithms. Remarkable acceleration is gained. Practical implications - The numerical method provides theoretical and technical support to accelerate resolving convection diffusion, non-equilibrium radiation diffusion and radiation transport problems. Originality/value - The FI schemes and iterations for the convection diffusion problem are proposed with their properties rigorously analyzed. The induction hypothesis reasoning method here differs with those for linearization schemes and is applicable to other nonlinear problems.
机译：目的-本文旨在为非线性对流扩散方程提供一个行为良好的非线性方案和加速迭代，并说明其基本性质。设计/方法/方法-研究非线性有限差分方案，并使用全隐式（FI）离散化来获得精确的仿真。设计具有二次收敛比率的Picard-Newton（PN）迭代以实现快速解决方案。使用离散函数分析技术进行理论分析。通过采用一种新颖的归纳假设推理技术，尽管由于保守扩散和对流算子的结合而产生了困难，但仍证明了该方案的L〜∞（H〜I）收敛性。因此建立其他属性。此外，该算法从一阶时间精度扩展到了二阶时间精度。研究结果-理论分析表明，两种FI方案都是稳定的，其解是唯一的，并且具有二阶空间和一阶/二阶时间精度。相应的PN迭代具有相同的精度和二次收敛速度。数值测试验证了结论，并证明了算法的高精度和高效率。获得了显着的加速度。实际意义-数值方法为加速解决对流扩散，非平衡辐射扩散和辐射传输问题提供了理论和技术支持。独创性/价值-提出了对流扩散问题的FI方案和迭代，并对其性能进行了严格分析。这里的归纳假设推理方法与线性化方案的归纳假设推理方法不同，并且适用于其他非线性问题。

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