In this paper, the space-time generalized finite difference scheme is proposed to effectively solve the unsteady double-diffusive natural convection problem in the fluid-saturated porous media. In such a case, it is mathematically described by nonlinear time-dependent partial differential equations based on Darcy's law. In this work, the space-time approach is applied using a combination of the generalized finite difference, Newton-Raphson, and time-marching methods. In the space-time generalized finite difference scheme, the spatial and temporal derivatives can be performed using the technique for spatial discretization. Thus, the stability of the proposed numerical scheme is determined by the generalized finite difference method. Due to the property of this numerical method, which is based on the Taylor series expansion and the moving-least square method, the resultant matrix system is a sparse matrix. Then, the Newton-Raphson method is used to solve the nonlinear system efficiently. Furthermore, the time-marching method is utilized to proceed along the time axis after a numerical process in one space-time domain. By using this method, the proposed numerical scheme can efficiently simulate the problems which have an unpredictable end time. In this study, three benchmark examples are tested to verify the capability of the proposed meshless scheme.

为了有效解决流体饱和多孔介质中的非定常双扩散自然对流问题，本文提出了时空广义有限差分格式。在这种情况下，它通过基于达西定律的非线性时间相关偏微分方程进行数学描述。在这项工作中，时空方法结合使用了广义有限差分法、Newton-Raphson 法和时间推进法。在时空广义有限差分格式中，可以使用空间离散化技术来执行空间和时间导数。因此，所提出的数值方案的稳定性由广义有限差分法确定。由于这种数值方法的性质，它基于泰勒级数展开和移动最小二乘法，得到的矩阵系统是一个稀疏矩阵。然后，使用Newton-Raphson方法有效地求解非线性系统。此外，利用时间推进法，在一个时空域中进行数值处理后，沿时间轴进行。通过使用这种方法，所提出的数值方案可以有效地模拟具有不可预测的结束时间的问题。在这项研究中，测试了三个基准示例以验证所提出的无网格方案的能力。通过使用这种方法，所提出的数值方案可以有效地模拟具有不可预测的结束时间的问题。在这项研究中，测试了三个基准示例以验证所提出的无网格方案的能力。通过使用这种方法，所提出的数值方案可以有效地模拟具有不可预测的结束时间的问题。在这项研究中，测试了三个基准示例以验证所提出的无网格方案的能力。