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FDPDE is a MATLAB toolbox for solving 2-D partial differential equations (PDEs) by means of a finite difference approach. FDPDE is designed to be easy to use for modeling simple 2-D heat transfer and diffusion problems.
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FDPDE has a graphical interface that allows users to draw 2-D problem domains, to set various conditions on boundaries, to choose either steady-state or time dependent PDEs to be solved, and to set the spacing of the finite difference grid and the time steps with initial conditions. The figure to the right shows construction in progress of a trapezoidal shape with a circular hole.
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Click to view full size
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Once the user draws the boundaries of the domain, the user selects the type of PDE and sets values for parameters in the PDE. The two types of PDEs that FDPDE solves are elliptic PDEs for steady-state problems, and parabolic PDEs for time dependent problems. For heat transfer problems, the user can set the thermal conductivity, density and heat capacity properties.
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The user can also set the types of conditions on each boundary. For heat transfer problems, the temperature on a boundary or the heat flux across a boundary may be set. The user may also specify that the boundary be insulated, or that the boundary is exposed to an external environment where the ambient temperature and heat transfer coefficient are specified.
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The user chooses the spacing for the finite difference grid. If the problem is time dependent, the user also sets initial conditions and the time steps for which solutions are calculated. Then the solver is run. |
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FDPDE lays a rectangular grid over the problem domain. The spacing is chosen by selecting the number of rows and columns of the finite difference grid. The finite difference nodes are at the intersections of these grid rows and columns. Only nodes that lie within the domain are used. Nodes on boundaries are placed at intersections of the rectangular grid with boundary lines. The grid to the right has 20 grid rows and 26 grid columns.
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After solving, a number of viewing options are available. Shown to the left is the temperature distribution plot. The upper boundary was held at 0º, the lower boundary was held at 200º, and all other boundaries were insulated. The colors and number of contours shown can be adjusted. If the problem is time dependent, the time step for the plot may also be specified.
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| For time dependent problems, movies can be generated showing the evolution of the temperature distribution over time.
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Users can draw a path across the distribution plot to view the profile of the field along the path as shown below.
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For time dependent problems, users can plot the field at a point over the time of the solution. Users can select the point by clicking in the distribution plot.
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Analogous diffusion problems can also be solved.
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