What are the limitations of the Explicit Finite Difference Model?

In summary, the limitations of the Explicit Finite Difference model for calculating 2D heat diffusion through an aluminum plate include potential errors due to the stability criterion, lack of guaranteed convergence to a solution, and varying convergence rates. It also requires significant computing resources and may have unexpected results when using an accelerating factor. Additionally, it may not handle boundary conditions as effectively as other methods, such as the finite element method. Other methods may have advantages over the EFD method, and further research and reading on the topic is recommended.
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Homework Statement:: Discuss the limitation of the Explicit Finite Difference Model.
Relevant Equations:: no formula

Hello there, I have to discuss the limitations of using the Explicit Finite Difference model to calculate a 2D Heat Diffusion through an aluminium place, however, I really don't understand what exactly it is asking me fore but I am guessing it has something to do with the stability criterion and I wanted seconds opinions.

[Moderator's note: moved from a homework forum.]
 
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Ask yourself:

What do you think can go wrong if you use it? Will always go right?

Will it always converge to a solution? Why? Or why not?

How quickly does it converge towards a solution?

How much computing resource does it use?

If you speed it up using an accelerating factor what may happen (IIRC you add, say, 1.2x the average of the adjacent points instead of just the average, where 1.2 is the accelerating factor)?

How does it handle boundary conditions?

Against which other methods are you comparing its limitations? - eg the finite element method?

What advantage do other methods have over the Explicit Finite Difference method - the EFD method has these as limitations.

Did you read the paper I pointed you to in your post Matlab report help please (Finite Difference Method)?

A web search will find answers to all these questions. A search in this forum will also find much useful information.
 
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1. What is the Explicit Finite Difference Model?

The Explicit Finite Difference Model is a numerical method used to solve partial differential equations. It involves discretizing the domain into a grid and approximating the derivatives at each grid point using finite difference formulas. This allows for the problem to be solved iteratively, with the solution at each time step depending only on the previous time step.

2. What are the limitations of the Explicit Finite Difference Model?

One limitation of the Explicit Finite Difference Model is that it can only be used for problems with simple geometries and boundary conditions. It also requires a fine grid resolution to accurately capture steep gradients, which can be computationally expensive. Additionally, it is only stable for certain combinations of time and space step sizes, which can restrict its applicability.

3. How does the Explicit Finite Difference Model compare to other numerical methods?

The Explicit Finite Difference Model is relatively simple to implement and can be used for a wide range of problems. However, it is less accurate than other numerical methods such as the Implicit Finite Difference Model or the Finite Element Method. It also has more limitations in terms of the types of problems it can solve.

4. Can the Explicit Finite Difference Model handle problems with changing boundary conditions or complex geometries?

No, the Explicit Finite Difference Model is not suitable for problems with changing boundary conditions or complex geometries. This is because the grid used in the model is fixed and cannot be easily adapted to changes in the problem. In these cases, other numerical methods such as the Finite Element Method may be more appropriate.

5. Are there any ways to overcome the limitations of the Explicit Finite Difference Model?

Yes, there are some techniques that can be used to improve the accuracy and stability of the Explicit Finite Difference Model. These include using adaptive grids, using higher-order finite difference formulas, and incorporating stability criteria into the choice of time and space step sizes. However, these techniques may also increase the computational cost of the model.

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