Quenching characteristics based on the two-dimensional (2D) nonlinear unsteady convection-reaction-diffusion equation are creatively researched. The study develops a 2D compact finite difference scheme constructed by using the first and the second central difference operator to approximate the first-order and the second-order spatial derivative, Taylor series expansion rule, and the reminder-correction method to approximate the three-order and the four-order spatial derivative, respectively, and the forward difference scheme to discretize temporal derivative, which brings the accuracy resulted meanwhile. Influences of degenerate parameter, convection parameter, and the length of the rectangle definition domain on quenching behaviors and performances of special quenching cases are discussed and evaluated by using the proposed scheme on the adaptive grid. It is feasible for the paper to offer potential support for further research on quenching problem.

中文翻译：

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二维淬火型对流反应扩散方程的自适应高阶有限差分分析

创造性地研究了基于二维（2D）非线性非定常对流反应扩散方程的淬火特性。该研究开发了一种二维紧致有限差分方案，该方案通过使用第一和第二个中心差分算子来近似一阶和二阶空间导数，泰勒级数展开规则以及提醒校正方法来近似三阶构造。阶空间导数和四阶空间导数，以及离散化时间导数的正向差分方案，这带来了准确性。退化参数，对流参数，在自适应网格上，利用所提出的方案，讨论和评估了矩形定义域的长度对淬火行为和特殊淬火性能的影响。本文为淬火问题的进一步研究提供了潜在的支持。