CLSVOF

A coupled level set volume of fluid method is being implemented in the incompressible code for interface tracking.

Serial Algorithm

Loop over elements (find the elements containing interface pieces)

1. Tag each element as incomplete

 Need a tag for elemental completeness

2. Truncate volume fractions so they’re 0 ≤ F ≤ 1

 Volume fraction is the second scalar
 

3. If 0 < F < 1 (element contains interface)

3.a. Use advected φ at element nodes to find interface slope for the element

 For tetrahedra, find the points at which the interface intersects the edges
 Use those three points (defining the plane) to find the interface normal

3.b. Move interface along normal until computed F = advected F

 Depending on which side of the interface is a tetrahedron, F is either the volume of the interface tetrahedron or the volume of the element minus the interface tetrahedron.
 

For a tetrahedron with vertices a, b, c, and d, the volume is: <math>V = \frac { |(\mathbf{a}-\mathbf{d}) \cdot ((\mathbf{b}-\mathbf{d}) \times (\mathbf{c}-\mathbf{d}))| } {6}.</math>

3.c. Use established interface to compute φ at each node and tag those nodes as reconstructed

 At each node, φ is the distance to the nearest point, unless two points are equidistant.
 Need a tag for nodal completeness/reconstruction

3.d. If any node has already been reconstructed, φ is min (other element reconstruction, this element reconstruction) (ensure that φ is min to interface everywhere)

3.e. Mark the element as complete

3.f. Loop over elements adjacent by shared faces - If it’s not marked as complete and not an interface element, add it to the reconstruction list

 Need reconstruction list
 Need data structure of each element's faces
 Need data structure of which two elements are adjacent to each face

While reconstruction list is not empty, loop over the reconstruction list (establish and walk out φ)

N_fixed = 0

If at least 3 nodes are tagged as reconstructed

Compute gradient of φ for the element using the three smallest values of reconstructed φ

If computed gradient is very different from advected gradient (nearest interface is not the one walked out from)

Skip the element and move on to next in the list

Else

Compute φ at all other nodes

If a node is tagged as reconstructed, φ = min (current value, new computed value)

Else φ = computed value, node is tagged as reconstructed

Mark the element as complete

Loop over elements adjacent by shared faces

If the adjacent element is not marked as complete, and not in the reconstruction list, and reconstructed φ of shared nodes is < nε add it to the list (stop adding nodes when > nε from interface)

Remove the element from the reconstruction list

N_fixed = N_fixed + 1

Else (element has only 1 or 2 reconstructed nodes)

Skip the element and move on to next in list

If N_fixed ≠ 0, go to start of loop

Else N_fixed = 0 and list is not empty, loop again through the list (less accurate method)

If reconstructed nodes ≤ 2

For each node not yet reconstructed, φ = min (distance to adjacent node + reconstructed φ of that node)

(Do we typically have full nodal adjacency(all nodes that share an edge or element with a node)?)

Mark the element as complete

Loop over elements adjacent by shared faces

If it’s not marked as complete, and not in the reconstruction list, and reconstructed φ of shared nodes is < nε add it to the list (stop adding nodes when > nε from interface)

Remove the element from the reconstruction list

N_fixed = N_fixed + 1

Else (at least 3 nodes are tagged as reconstructed)

Handle element as above

N_fixed = N_fixed + 1

When list is empty, for all elements not tagged as reconstructed, φ = nε for all nodes not tagged as reconstructed