advection

A method to solve an advection equation of a physical quantity (for example, volume fraction of fluid in a grid cell) for an identification of the water surface is effective to reduce computational load of the interface tracking.

From this general solution, the exact pdf for the two-mode nonlinear advection equation has been found by solving Liouville's equation [solution displayed in (ES23)].

Here, we use the unsteady linear advection equation as a model equation and discretize this with a finite volume scheme and the implicit Euler method.

For instance, the FFD has significant numerical diffusion due to the linear interpolation used in the semi-Lagrangian solver for the advection equation.

The fractional volume is then computed and updated at each time step using the following advection equation

In this method, the energy equation is decomposed into an advection equation and a diffusion equation as follows [8]

The advection equation is then solved and the flow front position updated.

The air/skin polymer interface and skin/core polymer interface are traced by pseudo-concentration method and governed by two advection equations separately in the literatures [21, 22], At each time step, the advection equations are coupled with the governing equations of the two polymer melts, respectively.

While solving the governing equations with the convective term, the mesh velocity is introduced to the material time derivatives of advection equations as follows: