### 4.4.1. Mesh Re-Initialization During Remeshing

The following points are important to note during remeshing:

- The total mesh displacement variable is relative to a specific mesh topology. Because the mesh topology changes, this variable is reset each time remeshing occurs.

- The new variable called `total centroid displacement` tracks the displacement of each boundary’s centroid since the beginning of the analysis (that is, relative to the original mesh).

- The specified displacement based mesh motion is relative to the initial mesh and must therefore include an offset to account for mesh re-initialization. The `Mesh Initialisation Time` variable corresponds to the time at which mesh re-initialization last occurred. This can be used to evaluate the required offset for time varying mesh displacement.

Note: `Total Centroid Displacement` is the sum of total mesh displacement and an offset vector. The value of the offset is determined by the displacement of the boundary’s centroid from its original position to its initial position. When using `Total Centroid Displacement` in a non-remeshing case, the original and the initial position are the same, resulting in an offset value of zero. In this case, there seems to be no difference between the variables, `Total Centroid Displacement` and `Total Mesh Displacement`. However, when using `Total Centroid Displacement` in a remeshing case, the original position is defined at the start of the simulation, while the initial position is defined after the last remesh; this results in an offset contribution that is non-zero.

An example of the expressions used to evaluate an applied displacement that includes the required offset to account for mesh re-initialization is given below. In this example, the applied displacement is evaluated as the desired displacement minus the value of the desired displacement at the `Mesh Initialisation Time`.

    Disp Desired = 1[m]*0.5*(1-cos(2.[s^-1]*pi*t))
    Disp Mesh ReInit = 1[m]*0.5*(1-cos(2.[s^-1]*pi*Mesh Initialisation Time ))
    Disp Applied = Disp Desired - Disp Mesh ReInit

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