Joce
• Member for 6 years, 3 months
• Last seen more than a month ago

That's a modelling problem, not a CS one. This will depend on what is diffusing and on the reasons why 2D is relevant. You may want to give physical details and ask this on physics.SE. Alternatively ...

A generic way of looking up the element in which a point of given coordinates may be is to sort them into a quadtree (octree in 3D). The leaves of the tree will contain only element having an ...

This is not just a "numerical discontinuity". Are you sure that this is the problem you want to solve? $\Phi$ looks like a phase, which is defined up to $2\pi$. That may be what you refer to as "...

With the continuity eqn only, you are missing all the mechanical balance: viscous and/or inertial effects will decide of the streamlines of such a flow. If your major aim is to keep it as simple as ...

This problem also arises in 2D, when all the vertices of a triangle lie on the boundary. And Stokes problem is not the only problem which may fail with such meshes, a $p$-Laplacian problem for some ...

Have you thought of barycentric coordinates? There is a unique way to write $x=\alpha A + \beta B$ with $\alpha+\beta=1$. Barycentric coordinates are usually employer in larger dimensions, but seem ...

Free surfaces occur when there are several phases present with sharp(ish) interfaces free to move. Some methods allow to treat all the phases as a single mathematical problem (e.g. level set or phase ...

For the fluid->particle problem, @AbhilashReddyM gave you the answer, the boundary condition will give you the value of $v_x$ at the boundaries. For the particle->fluid problem, yes, it is a boundary ...