Field3D.compute_tau_r

Field3D.compute_tau_r(self, mode='Smag', save_tensor_components=True):

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Description

Computes the anisotropic part of the residual stress tensor, denoted as $\tau_r$, for a given field in computational fluid dynamics simulations. The function can operate in two modes: 'Smag' and 'DNS'.

Parameters

• ValueError: If the field is not a filtered field (i.e., self.filter_size == 1).

• AttributeError: If required attributes (Cs, S_LES, DNS_folder_path) are not defined.

Raises

• mode (str, optional): Mode of operation, either 'Smag' for the Smagorinsky model or 'DNS' for Direct Numerical Simulation data. Default is 'Smag'.

Returns

None

Workflow

1. Initial Setup and Validation:

   • The function starts by updating the field and checking if the field is filtered.

   • If (self.filter_size == 1), it raises a (ValueError) because residual quantities computation only makes sense for filtered fields.

2. Mode: 'Smag' (Smagorinsky Model):

   • Turbulent Viscosity:

     • Checks if the Smagorinsky constant ((Cs)) is defined. If not, it initializes (Cs) to 0.1.

     • Computes the turbulent viscosity ((\mu_t)) using: $\mu_t = (Cs \cdot \Delta \cdot l)^2 \cdot S_{LES}$ where $\Delta$ is the filter size, $l$ is the grid size, and $S_{LES}$ is the strain rate at LES scale.

   • Anisotropic Residual Stress Tensor:

     • Initializes $\tau_r$ as a zero matrix.

     • For each component ((i, j)) of the tensor:

       • Computes $\tau^r_{ij} = -2\mu_t S_{ij}^{LES}$.

       • Adjusts for compressibility by subtracting the isotropic part $(S_{iso}) when (i = j)$.

       • Computes the squared components and accumulates them.

       • Saves the computed $\tau^r_{ij}$ to a file.

3. Mode: 'DNS' (Direct Numerical Simulation):

   • DNS Data Setup:

     • Checks if the path to DNS data is defined.

     • Initializes a (DNS_field) object to read DNS data.

     • Determines the type of filter used (box or Gaussian).

   • Residual Kinetic Energy:

     • Computes residual kinetic energy ( K_r^{DNS} ) as: $K_r^{DNS} = 0.5 \left( U_x^2 + U_y^2 + U_z^2 \right)_{DNS} - 0.5 \left( U_x^2 + U_y^2 + U_z^2 \right)$

     • Saves ( K_r^{DNS} ) to a file.

   • Anisotropic Residual Stress Tensor:

     • Initializes (\tau_r) as a zero matrix.

     • For each component $(i, j)$ of the tensor:

       • Computes the filtered product $\widetilde{(U_i U_j)}_{DNS})$

       • Calculates $\tau^r_{ij}$ as: $\tau^r_{ij} = \widetilde{(U_i U_j)}_{DNS} - \widetilde{U}_i \widetilde{U}_j - \delta_{ij} \frac{2}{3} K_r^{DNS}$

       • Computes the squared components and accumulates them.

       • Saves the computed $\tau^r_{ij}$ to a file.