In this work we present a Reduced Basis VMS-Smagorinsky Boussinesq model, applied to natural convection problems in a variable height cavity, in which the buoyancy forces are involved. We take into account in this problem both physical and geometrical parametrizations, considering the Rayleigh number as a parameter, so as the height of the cavity. We perform an Empirical Interpolation Method to approximate the sub-grid eddy viscosity term that lets us obtain an affine decomposition with respect to the parameters. We construct an a posteriori error estimator, based upon the Brezzi–Rappaz–Raviart theory, used in the greedy algorithm for the selection of the basis functions. Finally we present several numerical tests for different parameter configuration.

在这项工作中，我们提出了一个简化的基础VMS-Smagorinsky Boussinesq模型，该模型适用于涉及浮力的可变高度空腔中的自然对流问题。我们在这个问题中考虑了物理参数和几何参数，将瑞利数作为参数，并将腔的高度作为参数。我们执行经验插值方法来近似子网格涡流粘度项，从而使我们可以获得关于参数的仿射分解。我们基于Brezzi-Rappaz-Raviart理论构造一个后验误差估计器，用于贪婪算法中选择基础函数。最后，我们提出了几种针对不同参数配置的数值测试。