What is grid automatic generation?
Grid generation is to divide a specific research area into many small sub-areas (elements) to meet some specific requirements. In an ideal world, the shape and distribution of each element in the mesh can be determined by an automated mesh generation algorithm.
Algebraic mesh generation method and differential equation method for structural mesh generation
Delaunay generation method for unstructured mesh generation and front push mesh generation method, bold style , etc.
What is the difference between structured grid and unstructured grid?
According to the connection relationship of the grid , there are two main categories: structured grid and unstructured grid.
Structured grid mainly means that for each grid node , the number of connections to other adjacent nodes is certain or regular. For some grids , there may be a line where the number of connections between some nodes and other nodes is different. .
Unstructured grid means that the connection relationship between each grid node and other nodes is uncertain or irregular .
Figure 1 gives a simple example of a grid with two different forms. In some cases, part of the entire grid can be structured and another part unstructured. For example, in a river basin, the grid on the boundary is structured and the interior of the basin is unstructured.
What does pde mean?
PDE : Partial differential equation .
PDE contains equations of partial derivatives (or partial differentials) of unknown functions. The highest order of the partial derivative of the unknown function appearing in the equation is called the order of the equation.
The most widely used in mathematics, physics and engineering technology are second-order partial differential equations. It is customary to call these equations mathematical physics equations.
What does mesh generation technology do?
In computational fluid dynamics, a set of discrete points distributed in a flow field according to certain rules is called a grid , and the process of generating these nodes is called grid generation .
Grid generation is the link between geometric models and numerical algorithms . The geometric model can only be numerically solved when it is divided into a certain standard grid. Generally speaking, the denser the mesh, the more accurate the results will be, but the more time-consuming it will be. The accuracy and efficiency of numerical calculation results mainly depend on the grid and the algorithm used for division. It and the solution of the control equations are the two most important links in numerical simulation. Grid generation technology has developed into an important branch of fluid machinery CFD. Existing grid generation methods are mainly divided into three categories: structured grids, unstructured grids and hybrid grids .
According to the type of partial differential equations, it can be divided into mesh generation methods for solving elliptical partial differential equations , solving hyperbolic partial differential equations and solving parabolic partial differential equations.
Grid generation and solution technology are key to computational fluid dynamics numerical simulations
What is CFD ?
Computational Fluid Dynamics (CFD) is a discipline that uses discretized grid technology and numerical calculation methods to solve flow control equations.
What are partial differential equations
Given the partial differential expression, we need to find the original function
Specifically, the research content of grid generation is how to reasonably divide a given geometric area into a combination of a limited number of basic geometric units (grid units). For two-dimensional areas, these basic geometric units are usually triangles, quadrilaterals or arbitrary polygons ; for three-dimensional areas, the units mainly include tetrahedrons, hexahedrons, etc. The generated mesh discretizes a continuous physics problem with infinite degrees of freedom into a large-scale discrete system with limited degrees of freedom.
The numerical solution method of partial differential equations converts the governing equations of the original solution into discrete forms , and uses numerical methods to find numerical approximate solutions at a limited number of discrete points in the computational domain. In this process, the discretization process is called computational grid generation, which is a necessary "pre-processing" work for computational fluid dynamics numerical simulations to be carried out.
The topology of COH is exactly the same and can be stored using the same data structure.
-----------------------------------------------I am the dividing line --------------------------------------------------
Since my book didn't arrive, I can only listen to the CFD online class first (I lost the notes I took!! Cry!!!) Recently
I watched The Mortal's Cultivation of Immortality, hahahahaha, it's so interesting (the anime version of Han Li becomes more and more handsome the more I watch it hahaha)
Return to the topic
and continue taking notes as you read before.
Mainly consider the inviscid equation
Partial differential equations can be divided into several categories: hyperbolic, parabolic, elliptic
Euler equation characteristics: time derivatives; space derivatives and C.
In the two-dimensional space, the most linearly independent vector number is 2; (if it is 3, it can be The other two vectors (linearly independent) are pieced together)
n-dimensional space: any vector can be represented by a linear combination of n basis vectors
Properties of dot product:
Cross product: Although it is represented by a determinant, the calculation is still a vector (the cross product is perpendicular to the plane corresponding to u and v) right-hand determination and
length (?)
mixed product: obtained It’s also a number
Find P1 P2
Record the finite volume method
The finite volume method can be used for structured grids and unstructured grids;
the finite difference method is more suitable for structured grids.
Finite volume method
is conservative and suitable for irregular shapes
f is the proxy, A b is known, A is the coefficient matrix obtained after discretization, A is the square matrix
A matrix must not be 0 after discretization
A grid has only one fai value, which is how many grids correspond to how many fai values.
b is the result matrix, sometimes also called the source term.
