Description
Computational Fluid Dynamics (CFD) is a branch of engineering that uses numerical methods and algorithms to model and analyze fluid flow problems. The MacCormack and Rusanov methods are two important numerical methods in CFD used to solve the partial differential equations governing fluid flow.
MacCormack Method
The MacCormack method is a second-order accurate numerical method used to solve hyperbolic equations such as the Euler equations. This method consists of two steps:
- Predictor step: In this step, the values of the flow variables at the next time step are estimated using a forward difference scheme.
- Corrector step: In this step, the predicted values are corrected to create a backward difference scheme. The arithmetic mean of the predicted and corrected values is considered as the final value at the next time step.
Advantages of the MacCormack method:
-
- Simplicity of implementation
- High accuracy for many problems
- Good stability for small Courant numbers
Disadvantages of the MacCormack method:
-
- May be unstable for large Courant numbers
- May not have sufficient accuracy for complex flows
Rusanov Method
The Rusanov method is a first-order accurate numerical method used to solve hyperbolic equations using a viscous numerical flux. This method is very suitable for flows with steep gradients and shocks.
Advantages of the Rusanov method:
-
- High stability for large Courant numbers
- Suitable for flows with steep gradients
- Simple implementation
Disadvantages of the Rusanov method:
-
- Lower accuracy compared to the MacCormack method
- More numerical diffusion
Comparison of MacCormack and Rusanov Methods
The purpose of Computational Fluid Dynamics (CFD) is to analyze systems including fluid flow, heat transfer and related phenomena, based on computer simulation. In this science, the governing equations of fluid flow are continuity and Navier-Stokes equations, and the goal is to discretize them. Mac, Cormac, Rusanov methods are one of the most reliable methods for solving flow numerically in CFD. It has been addressed in this research.
The purpose of this project is to solve the wave equation using the computational fluid dynamics method (Mac Cormac, Rusanov methods) and compare the results with the exact solution. It should be mentioned that the entire project has been done with the help of Fortran programming language. By preparing this project, the code of all the methods along with the results will be available to you.
To purchase this project or get more information, please follow the link below.