## Lecture 4: Advecting Interfaces

Simulations of immiscible multifluid flows with a sharp interface:
Require the use of moving grids
Require the advection of a marker function identifying the different fluids
Require constant density and viscosity in each fluid
Require us to assume the flow is incompressible
None of the above

Advection of discontinuous marker function by linear schemes
Always leads to oscillatory solutions
Always leads to excessively diffused solution
Always leads to either oscillatory or diffused solution
Always produces a sharp discontinuity
None of the above

Specialized methods designed to advance a discontinuous marker function include
The Volume of Fluid and Level Set methods
The finite element method
Finite volume methods
Spectral methods
All of the above

For one-dimensional advection of a discontinuous marker function the Volume of Fluid Method
Gives the exact solution
Works by preventing numerical diffusion
Requires the reconstruction of the discontinuity
Modifies the flux between cells
All of the above

For two and three-dimensional advection of a discontinuous marker function the Volume of Fluid Method
Gives the exact solution
Uses an interface that is aligned with grid lines
Requires the reconstruction of the discontinuity
Uses marker particles to follow the interface
Identifies the interface as the zero contour of the marker function

To reconstruct the interface in a cell in Volume of Fluid Method we need
The volume fraction in each cell
The normal to the interface
The normal and the volume fraction
The normal or the volume fraction
None of the above

For two and three-dimensional advection of a discontinuous marker function, the Level Sets method
Gives the exact solution
Uses marker particles to follow the interface
Identifies the interface as the zero contour of the marker function
Advects the marker function directly
None of the above

In the level set method the
Marker function is constructed from the level set function
The level set function must be adjusted continuously
The level set function is generally taken to be the distance function
The level set function is distorted by the flow
All of the above

Front tracking methods
Gives the new interface location exactly
Track the interface with connected marker points
Requires the use of triangulated interface mesh
Require the use of separate grids for each fluid
All of the above

The marker function is updated indirectly by
Level Set methods only
Volume of Fluid methods only
Front Tracking and Level Set methods
Level Set and Volume of Fluid methods
None of the above