Grashof Number–Rayleigh Number Correlation

They are governing parameters for natural convection. Fundamental dimensionless numbers used for flow transition judgment and heat transfer coefficient correlation equations.

We use spatial discretization by the Finite Element Method (FEM). We assemble the element stiffness matrix and construct the global stiffness equation.

We perform transformation to the weak form (variational form) and use formulation by the Galerkin method using test functions and shape functions. The choice of element type (low-order elements vs. high-order elements, full integration vs. reduced integration) directly affects the trade-off between solution accuracy and computational cost.

We solve the simultaneous equations using direct methods (LU decomposition, Cholesky decomposition) or iterative methods (CG method, GMRES method). For large-scale problems, preconditioned iterative methods are effective.

Developed by Fluent Inc. Acquired by Ansys in 2006. A general-purpose CFD solver based on unstructured grids.

Current affiliation: Ansys Inc.

Developed by CD-adapco. Acquired by Siemens in 2016 and integrated into the Simcenter brand. Known for polyhedral meshes.

Current affiliation: Siemens Digital Industries Software

Founded in Sweden in 1986. Started as FEMLAB with MATLAB integration, later renamed to COMSOL. Strong in multiphysics.

Current affiliation: COMSOL AB

When converting models between different solvers, attention is needed to the correspondence of element types, compatibility of material models, and differences in the representation of loads and boundary conditions. Particularly, high-order elements and special elements (cohesive elements, user-defined elements, etc.) often cannot be directly converted between solvers.