Write a new initial condition inside a kernel

The purpose is to implement one initial condition for the phase-field \(\phi\) such as it represents a circular (2D) or spherical (3D) bubble at the beginning of the simulation. We need to implement the following equation:

(246)\[\phi(\boldsymbol{x},0)=\frac{1}{2}\left[1+\tanh\left(\frac{2(r_0-d_{0})}{W}\right)\right]\]

where \(r_0\) is bubble radius and the distance \(d_0\) is defined by

(247)\[d_{0}=\sqrt{(x-x_{0})^{2}+(y-y_{0})^{2}+(z-z_{0})^{2}}\]

where \(\boldsymbol{x}_0=(x_0,y_0,z_0)\) is the center position of the bubble and \(\boldsymbol{x}=(x,y,z)\) is one particular node on the mesh.

Implement your initial condition

You must modify three files which are in the folder: Models_NS_AC_Comp.h, LBMScheme_NS_AC_Comp.h and LBM_enums.h.

Edit the file with command:

$ cd LBM_Saclay_Rech-Dev/src/kernels/NSAC_Comp
$ geany Models_NS_AC_Comp.h

  1. Read the input parameters

    In this file, the input parameters \(r_0\), \(x_0,y_0,z_0\) must be read from the .ini file. Add e.g. between lines 97 and 206

    ModelParams(const ConfigMap &configMap, LBMParams params) {
...
...
x0 = configMap.getFloat  ("init", "x0", 0.0);
y0 = configMap.getFloat  ("init", "y0", 0.0);
z0 = configMap.getFloat  ("init", "z0", 0.0);
r0 = configMap.getFloat  ("init", "r0", 0.2);

    The first line means that x0 must be read as a real in section [init]. If the line does not exist in the input file, then its value is 0.

  2. Declare them (between lines 309 and 341)

    ModelParams(const ConfigMap &configMap, LBMParams params) {
...
...

real_t x0, y0, z0, r0 ;

  3. Add a new keyword for that initial condition (e.g. between lines 234 and 271)

    else if (initTypeStr == "sphere")
   initType = PHASE_FIELD_INIT_SPHERE;

    The keyword sphere has to appear in the .ini file. The keyword PHASE_FIELD_INIT_SPHERE must be added in the list of enumerations (see below file LBM_enums.h).

  4. Definition of hyperbolic tangent function (line 349)

    KOKKOS_INLINE_FUNCTION real_t phi0(real_t x) const {
   return 0.5 * (1 + tanh(sign * 2.0 * x / W));
}

    The function phi0 implements the hyperbolic tangent function. It is defined in class Model.

Eq. (246) is implemented in file LBMScheme_NS_AC_Comp.h:

$ cd LBM_Saclay_Rech-Dev/src/kernels/NSAC_Comp
$ geany LBMScheme_NS_AC_Comp.h

  1. The initializations of macroscopic fields are performed in the function (line 1024):

    KOKKOS_INLINE_FUNCTION
void init_macro(IVect<dim> IJK, RANDOM_POOL::generator_type rand_gen) const {
   ...
}

    In that function, the following lines implement \(r_0-d_0\) for 2D or 3D cases:

    else if (Model.initType == PHASE_FIELD_INIT_SPHERE) {
     if (dim == 2) {
        xphi = (Model.r0 - sqrt(SQR(x - Model.x0) + SQR(y - Model.y0)));
     }
     else if (dim == 3) {
        xphi = (Model.r0 - sqrt(SQR(x - Model.x0) + SQR(y - Model.y0) + SQR(z - Model.z0)));
     }
        xc = xphi ;
     }

  2. Once \(r_0-d_0\) is defined (xphi), the hyperbolic tangent function is applied (line 1420)

    phi = Model.phi0(xphi);

Edit file LBM_enums.h

$ cd LBM_Saclay_Rech-Dev/src
$ geany LBM_enums.h

  1. Add the keyword PHASE_FIELD_INIT_SPHERE in the list of enumeration (line 111)

    enum PhaseFieldInit {
   ...

   PHASE_FIELD_INIT_SPHERE,

Compile, modify your .ini file and check

Section author: Alain Cartalade