Algorithm 1: Uzawa iterative algorithm [19].

Step 1. Find initial guess $({\mathbf{u}}_h^0,p_h^0,T_h^0)\in {\mathbf{M}}_h\times W_h\times Z_h$ by $$\begin{array}{c}\hfill \left\{\begin{array}{cc}& Pr(\nabla {\mathbf{u}}_h^0,\nabla \mathbf{v})-(p_h^0,\nabla ·\mathbf{v})=PrRa(\mathbf{j}{T}_h^0,\mathbf{v}),\forall \mathbf{v}\in {\mathbf{M}}_h,\hfill \\ & (\nabla ·{\mathbf{u}}_h^0,q)=0,\forall q\in W_h,\hfill \\ & \kappa (\nabla T_h^0,\nabla s)=(\gamma ,s),\forall s\in Z_h.\hfill \end{array}\right.\end{array}$$ Step 2. Given a relaxation parameter $\rho >0$, find $({\mathbf{u}}_h^{n+1},p_h^{n+1},T_h^{n+1})\in {\mathbf{M}}_h\times W_h\times Z_h$ as solution of $$\begin{array}{c}\hfill \left\{\begin{array}{cc}& Pr(\nabla {\mathbf{u}}_h^{n+1},\nabla \mathbf{v})+b_1({\mathbf{u}}_h^n;{\mathbf{u}}_h^{n+1},\mathbf{v})-(p_h^n,\nabla ·\mathbf{v})=PrRa(\mathbf{j}{T}_h^{n+1},\mathbf{v}),\forall \mathbf{v}\in {\mathbf{M}}_h,\hfill \\ & (p_h^{n+1},q)=(p_h^n,q)-\rho (\nabla ·{\mathbf{u}}_h^{n+1},q),\forall q\in W_h,\hfill \\ & \kappa (\nabla T_h^{n+1},\nabla s)+b_2({\mathbf{u}}_h^n;T_h^{n+1},s)=(\gamma ,s),\forall s\in Z_h.\hfill \end{array}\right.\end{array}$$