Reference no: EM132856636
Gray-Scott Reaction-Diffusion
Numerical method details
In order to solve this equation, you are asked to have a spatial resolution scheme of order 2 based on finite differences.You can choose the integration method in time of your choice.The mesh you need to use should be structured and uniform.The size of this is your choice.You will also have to define the ideal time step as well as the final time simulation.
Analysis requested
The constants of the diffusion coefficient of components A and B, denoted respectively DA DB, the coefficients of appearance of A (f) and disappearance of B (k), and the reaction rate kA have a significant impact on the results obtained. You are asked to compare and analyze the results you get based on at least two distinct variables of your choice, one of which must be either k or f.
For your initial analysis, you can use CA = 1mol/m3 over the entire domain Ω and initialize a zone of your choice to CB = 1mol /m3. We will apply a null initial condition for B for the rest of the domain, ie. CB = 0mol/m3. Additionally, use the following values to get started your analysis: DA = 10-5 m2 s , DB = 0.51 10-5 m2 s , kA = 1 m6 mol2 s , f = 0.03s -1 , k = 0.061s -1 . You will use a square domain for your initial analysis: Ω = [0, 1] × [0, 1].
From a numerical point of view, you are asked to demonstrate the convergence of your system in time and space. Justify your final choice of mesh as well as the integration method and the chosen time step.
Attachment:- Gray-Scott Reaction-Diffusion.rar
Attachment:- project.rar
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