Homework 3: Use the Fixed Grid --Volume of Fluid Method with Structured Cartesian CVFEM mesh To track Filling Front h=1 h = 0 2 r = 1 3 Hand in 1. Code 2. Plot of R(t) vs t 1<R<3 Use 3 time steps 3. Compare with analytical solution from Cylindrical cords. Note analytical sol Solution satisfying usual bc’s Sub in moving boundary mass balance Solution

Notes on Volume of Fluid Method for Filling For an arbitrary volume Flow balance gives Relate volume to control volume f is the volume of fluid VOF Use basic Numerical VOF assumption Filling or partially filled cells

Most modification is in Solution Subroutine Solution in a time step Old values of nodal VOF field known ----With initial setting ---- introduce modified coefficient set as follows ---- solve Initial settings Coding Following Meshing calculate and store coefficients and boundary treatments In identical fashion to steady state problem Also calculate Control volume volumes – Each element in the support of node i Contributes 1/3 of its volume to the control volume of i Pretty much our previous point by point steady state solver but with Modified RHS Will return h i =0 in empty and partially filled cells. Note extra source will ensure Smooth transition from partial to filled cell in a time step. ---After solver Update liquid fraction by NOTE we assume that h i = 0 in this update to correct this “error” we follow with The correction --- Repeat (10 time often enough) See One-D code in notes