%0 Journal Article
%T 基于原位燃烧模型的外梯度法<br>Extragradient Method Based on in Situ Com-bustion Model
%A 曹梦霖
%J Advances in Applied Mathematics
%P 3035-3046
%@ 2324-8009
%D 2022
%I Hans Publishing
%R 10.12677/AAM.2022.115323
%X 为了更好求解原位燃烧模型，给出了一种外梯度法。首先在离散格式上采用Crank-Nicolson中心差分方案，其次迭代算法选取外梯度法，将非线性互补问题通过投影转化为不动点方程的等价形式，进而使用外梯度法求解，最后给出该算法在满足线性收敛条件下的数值模拟结果，并与内点法进行比较，验证了该算法在解决原位燃烧模型的可行性。<br />
To better solve the in situ combustion model, an extragradient method is given. Firstly, the Crank-Nicolson central difference scheme is used in the discrete format, and secondly, the extra-gradient method is chosen for the iterative algorithm, which transforms the nonlinear complemen-tary problem into the equivalent form of the immobile point equation by projection, and then solves it using the extragradient method, and finally, the numerical simulation results of the algorithm are given under the condition of satisfying linear convergence, and compared with the inner point method to verify the algorithm in solving the in situ combustion. The feasibility of the algorithm in solving the in situ combustion model is verified.
%K 原位燃烧模型，非线性互补算法，外梯度法，偏微分方程<br>In Situ Combustion Model
%K Nonlinear Complementary Algorithm
%K Extragradient Method
%K Partial Differential Equations
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=51944