- Executive Title: "Getting Started$\text{CFD}$: User Manual$\text{Python}$and$\text{MATLAB}$For basic fluid dynamics simulation"
- Subtopic (Technical/Focus): "Writing Code$\text{Finite Difference}$and$\text{Finite Volume}$too$\text{Python/MATLAB}$For the equation$\text{Advection}$and$\text{Diffusion}$"
- Engaging Title: "Build Your Own Flow Model: Learn the Basics$\text{CFD}$pass$\text{Python}$and$\text{MATLAB}$"
2. 📝 Content Outline
This content will serve as an introductory guide focusing on the use of popular mathematical tools such as:$\text{Python}$and$\text{MATLAB}$To understand and apply the fundamental principles of computational fluid dynamics simulation ($\text{Computational Fluid Dynamics - CFD}$):
2.1. Get to know$\text{CFD}$and importance
- Definition: $\text{CFD}$It is the use of mathematics and numerical algorithms to solve equations that govern the movement of a fluid (such as air or water), such as the equations.$\text{Navier-Stokes}$
- Role in Engineering: Used in aircraft design, propellers, heat flow, and weather prediction.
- Why must$\text{Python}$and$\text{MATLAB}$: Both are excellent tools for numerical computing,$\text{Prototyping}$Fast and data visualization
2.2. Basics of solving equations using numerical methods
- $\text{Finite Difference Method (FDM)}$:
- Concept: It's the easiest way to get started.$\text{CFD}$By approximating the derivatives of a function with finite differences on a grid.
- Application: Solving simple heat transfer equations ($\text{Diffusion Equation}$) or the convection equation ($\text{Advection Equation}$)
- Tools: Use basic functions of$\text{NumPy}$in$\text{Python}$or$\text{Matrix Operations}$in$\text{MATLAB}$
- $\text{Finite Volume Method (FVM)}$:
- Concept: It is a widely used method in software.$\text{CFD}$Commercial, emphasizing conservation of quantity (Conservation) in each controlled volume (Control Volume).
- Application: Solving equations$\text{Navier-Stokes}$In a more complex form
2.3. Preliminary simulation in 1D and 2D
- $\text{1D Advection Equation}$(Convection equations in 1 dimension): It shows the basic problems of flow and the problems$\text{Numerical Diffusion}$That needs to be fixed
- Sample Code: Creating a Time Loop ($\text{Time-stepping}$) to see the movement of square waves ($\text{Square wave}$)
- $\text{2D Laplace/Poisson Equation}$: Demonstrate how to deal with boundary conditions and solve problems in 2D (e.g., flow around an object).
2.4. Display and evaluation of results
- Visualization tools:
- $\text{Python}$: Use the library$\text{Matplotlib}$or$\text{Mayavi}$For displaying 2D graphs,$\text{Contour Plots}$and$\text{Vector Fields}$
- $\text{MATLAB}$: Use function$\text{surf, contour, quiver}$In 3D and 2D display
- Stability Assessment: Condition Check$\text{Courant-Friedrichs-Lewy (CFL)}$To ensure that the numerical simulation is stable and error-free.
Core Field:
- $\text{CFD}$(Computational Fluid Dynamics), Fluid dynamics, Simulation engineering,$\text{Numerical Methods}$
Tools (Tools/Software):
- $\text{Python}$, $\text{MATLAB}$,$\text{NumPy}$,$\text{Matplotlib}$, Numerical Computing
Simulation Technique:
- $\text{Finite Difference Method}$ ($\text{FDM}$), $\text{Finite Volume Method}$($\text{FVM}$),$\text{Advection}$,$\text{Diffusion}$
Applied Mathematics:
- Partial differential equations ($\text{PDE}$),$\text{Navier-Stokes Equations}$,$\text{Boundary Conditions}$, stability ($\text{Stability}$)
Basic Application:
- $\text{1D Simulation}$,$\text{2D Simulation}$,$\text{Prototyping}$
