advection diffusion solution pde toolbox in matlab

To solve an advection-diffusion equation using the PDE Toolbox in MATLAB, you first need to set up the PDE problem by defining the coefficients of the equation. Here's a general outline on how to solve the advection-diffusion equation using the PDE Toolbox:

1. Define the advection-diffusion equation in the form of (\frac{\partial u}{\partial t} = \nabla \cdot (D\nabla u - \mathbf{v}u)), where (u) is the unknown field, (D) is the diffusion coefficient, (\mathbf{v}) is the velocity field, and (t) is time.

2. Create a PDE model using the createpde function.

3. Define the geometry of the problem using the geometryFromEdges function. You can create a 2D or 3D geometry.

4. Specify the coefficients of the PDE (diffusion and advection terms) using the specifyCoefficients function.

5. Set up the boundary conditions using the applyBoundaryCondition function.

6. Generate a mesh using the generateMesh function.

7. Solve the PDE using the solvepde function.

Here is a simple example to get you started on solving an advection-diffusion equation using the PDE Toolbox in MATLAB:

main.m
model = createpde();

geometryFromEdges(model, 'Square');

diffCoeff = 0.01;
vel = [1; 0];
specifyCoefficients(model, 'm', 0, 'd', diffCoeff, 'c', vel(1), 'a', 0, 'f', 0);

applyBoundaryCondition(model, 'dirichlet', 'Edge', 1:model.Geometry.NumEdges, 'u', 1);

generateMesh(model);

results = solvepde(model);
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This example sets up a simple 2D square domain with a constant diffusion coefficient and advection velocity in the x-direction. Adjust the coefficients, geometry, and boundary conditions according to your specific problem.

Remember to adjust the code based on your specific advection-diffusion equation and problem setup.