The basic operation methods of numerical simulation include finite element method, finite difference method, boundary element method and direct difference method. The finite element method (FEM) uses the variational principle and the weighted residual method to discretize the continuous solution domain into a group of finite element combinations for analytical simulation or approximation. It is suitable for the domain with complex geometry. With the continuous development of computer technology, the application software of finite element method emerges one after another and is widely used, such as ANSYS, MSC and other software used by our company at present, but its defect is that it is unable to carry out pre-processing and post-processing.
The finite difference method will be the first computer numerical simulation method, which is still widely used at present. In this method, the solution domain is divided into difference grids, and the original continuous solution domain is transformed into a finite number of grid nodes. In the finite difference method, Taylor series expansion and other methods are used. The values on grid nodes are expressed by algebraic equations, and the derivative in the governing equation is expressed as the difference quotient of function values on grid nodes. Its main characteristics are the adoption of mathematical concepts, intuitive expression, mature and reliable.
Boundary element method is also known as boundary integral equation method. As the name implies, it focuses on the boundary. It takes the boundary integral equation defined on the boundary as the control equation, and converts the boundary integral equation into a linear algebraic equation by calculating the difference value of discrete elements at the boundary. This method is especially suitable for the calculation of temperature field, but the mathematical model is more complex and the calculation environment is more limited.
The direct difference method was first produced in the 1970s and 1980s. Its core idea is that the difference replaces the differential, which is the basic starting point of the finite difference method. It is a method of numerical solution of differential equation and Integro differential equation.