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adwiteeymauri
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I want to compute the flux surfaces using FEM but i haven't found any good source to read. any help will be appreciated.
Thank you
Thank you
The Grad Shafranov equation is a partial differential equation used to describe the equilibrium of a plasma in a magnetic field. It is important in physics because it helps us understand the behavior of plasma in fusion reactors, which is crucial for developing sustainable energy sources.
The Finite Element Method is a numerical technique used to solve partial differential equations by dividing a complex problem into smaller, simpler elements. These elements are then solved individually and combined to find a solution for the entire problem. In the case of the Grad Shafranov equation, the magnetic field and plasma parameters are discretized and solved using the Finite Element Method.
The Finite Element Method allows for the solution of complex, non-linear equations with varying boundary conditions. It also allows for adaptability in the discretization, which is useful for solving problems with irregular geometry. Additionally, the Finite Element Method can handle different types of elements, making it a versatile approach for solving the Grad Shafranov equation.
One of the main challenges in using the Finite Element Method to solve the Grad Shafranov equation is the large number of unknowns that need to be solved. This can result in long computing times and can be computationally expensive. Additionally, the choice of elements and discretization can greatly affect the accuracy of the solution, so careful consideration must be taken in selecting these parameters.
There are several ways to validate the results obtained from solving the Grad Shafranov equation using the Finite Element Method. One method is to compare the results with experimental data or other analytical solutions. Another way is to perform convergence studies, where the solution is refined and compared to a known analytical solution to ensure accuracy. Sensitivity studies can also be done to test the robustness of the solution to changes in the input parameters.