Thermohaline convection (THC) in porous media is frequently investigated using the problem of porous enclosure. Most of the existing modeling‐based studies are limited to 2‐D simulations, because 2‐D assumption is widely used to deal with computational requirement of 3‐D numerical solutions. Analytical solutions serve as an alternative to deal with computational requirement of numerical solutions. Existing analytical solutions of THC are mostly limited to 2‐D and also under steady‐state regime. In this work, we develop a meshless 3‐D semianalytical solution for the problem of THC in a porous box under crossed thermal and solute gradients, for both steady state and transient regimes. The semianalytical solution is developed using the Fourier series (FS) method applied to the vector potential form of the governing equations. The extension to transient solutions represents an important technical feature of this work, as the applications of the FS method to density‐driven problems have been limited to steady‐state conditions. The FS solution is validated against a finite element solution obtained using COMSOL Multiphysics. Numerical experiments show the worthiness of the developed FS solution as a benchmark because it clearly allows making distinction between different numerical techniques. The effects of governing parameters on three‐dimensional THC have not been investigated previously. We perform a detailed parameter sensitivity analysis to address this gap. A vortex convective flow is observed and the orientation and intensity of the flow is sensitive to the gravity number. The increase in the temperature gradient reduces the salinity flux.

中文翻译：

---

多孔罩中瞬态三维热盐对流的傅里叶级数解

多孔介质中的热盐对流（THC）经常使用多孔外壳的问题进行研究。现有的大多数基于模型的研究仅限于二维模拟，因为二维假设被广泛用于处理三维数值解的计算要求。分析解决方案可以替代处理数值解决方案的计算要求。现有的四氢大麻酚的分析解决方案大多限于二维并且也处于稳态下。在这项工作中，我们针对稳态和瞬态两种情况，针对交叉热和溶质梯度下多孔箱中THC的问题，开发了无网格的3D半解析解决方案。使用应用于控制方程矢量势形式的傅里叶级数（FS）方法开发半解析解。瞬态解决方案的扩展代表了这项工作的重要技术特征，因为FS方法在密度驱动问题上的应用仅限于稳态条件。FS解决方案针对使用COMSOL Multiphysics获得的有限元解决方案进行了验证。数值实验显示了开发的FS解决方案作为基准的价值，因为它显然可以区分不同的数值技术。先前尚未研究控制参数对三维THC的影响。我们将进行详细的参数敏感性分析以解决这一差距。观察到涡流对流，并且流的方向和强度对重力数敏感。温度梯度的增加降低了盐度通量。