As the Immersed boundary method, i.e. the smoothed profile method (see Sec. 11.1.2) is a derived class of the Velocity Correction Scheme (VCS) (see Sec. 11.1.1 and Sec. 11.3), hence most of the setting introduced for the VCS is applicable for the SPM and hence will not be repeated here and only the unique options to the SPM will be discussed here.
For the SPM simulations, the property SolverType must be set to SmoothedProfileMethod,
while the immersed boundaries are defined in a function called ShapeFunction. Besides, the
property ForceBoundary can be set to True for a more accurate velocity profile inside the
body in expense of adding a slightly extra compressibility. Thus, the TIMEINTEGRATIONSCHEME
and SOLVERINFO section could be similar to:
1<TIMEINTEGRATIONSCHEME> 2 <METHOD> IMEX </METHOD> 3 <ORDER> 3 </ORDER> 4</TIMEINTEGRATIONSCHEME> 5 6<SOLVERINFO> 7 <I PROPERTY="SolverType" VALUE="SmoothedProfileMethod" /> 8 ... 9 <I PROPERTY="ForceBoundary" VALUE="True" /> 10</SOLVERINFO>
The ShapeFunction which defines the shape of immersed boundary must be defined in the
CONDITIONS section:
1<FUNCTION NAME="ShapeFunction"> 2 <E VAR="Phi" USERDEFINEDTYPE="TimeDependent" VALUE="..." /> 3 <E VAR="Up" VALUE="..." /> 4 <E VAR="Vp" VALUE="..." /> 5 ... 6</FUNCTION>
As a brief guideline, to define a cylinder of radius 0.5 and center at the point (0,0)
according to expression (11.11), the "Phi" field in the ShapeFunction function should
be:
1 <E VAR="Phi" USERDEFINEDTYPE="TimeDependent" VALUE="-0.5*(tanh((rad(x,y)-0.5)/0.04)-1.0)" />
where the scaling coefficient has been set to 0.04. The variable names are compulsory, being
Phi the shape of the bodies, and Up, Vp and Wp functions representing the velocity field inside
them. The attribute USERDEFINEDTYPE is compulsory only if the functions depend on time,
when it must be set to "TimeDependent".
For immersed boundaries with geometries that cannot be represented by means of analytical
functions, an .stl binary file can be supplied as well. However, the geometry file must be first
converted to .fld format with the phifile module of FieldConvert. The simplest way to
proceed is by issuing the command:
FieldConvert -m phifile:file=geom.stl:scale=value session.xml geom.fld
where the value of scale corresponds to the coefficient ξ in equation Eq. (11.11). More details
can be found in section 5.6.38. In any case, it is important to remark that this functionality is
still under development.
In the ShapeFunction block of the session file, the line <E VAR="Phi" ... /> indicates that
the immersed bodies are defined by the function introduced in VALUE, while a line like the
following:
1 <F VAR="Phi" FILE="geometry.fld" />
must be used when the Φ field is defined in an .stl file previously converted to .fld
format. In this case, the solver only supports non-moving geometries and the attribute
USERDEFINEDTYPE="TimeDependent", if specified, will not be used.