Fluid Mechanics#
This page presents the fluid mechanics analyses currently supported by OpenPisco and their corresponding mathematical formulations.
Overview#
At present, OpenPisco provides support for incompressible steady-state laminar fluid flow simulations through an interface with OpenFOAM.
Supported Analyses#
Incompressible steady-state laminar flow
Incompressible Steady-State Laminar Flow#
The flow is governed by the incompressible Navier-Stokes equations
\[\begin{split}\begin{equation}
\label{eq:steady_state_NS_incompressible}
\left\{
\begin{array}{rllll}
\text{div}(v) &=& 0 & \text{in} & \Omega_f,\\
-\text{div}(\sigma_f(v,p))
+ \rho \nabla v\,v
&=& f_f & \text{in} & \Omega_f,\\
v &=& v_0 & \text{on} & \partial\Omega^D_f,\\
\sigma_f(v,p)n &=& 0 & \text{on} & \partial\Omega^N_f,\\
v &=& 0 & \text{on} & \Gamma.
\end{array}
\right.
\end{equation}\end{split}\]
where:
\(\rho\) is the fluid density;
\(v\) is the velocity field;
\(p\) is the pressure field;
\(f_f\) is the density of volumic forces acting on \(\Omega_f\);
\(\sigma_f\) is the stress tensor of a Newtonian fluid.
The fluid stress tensor is defined as
\[\begin{equation}
\sigma_f(v,p)=2\mu e(v)-pI,
\end{equation}\]
where
\[e(v)=\frac{\nabla v + (\nabla v)^T}{2}\]
is the strain-rate tensor and \(\mu\) denotes the dynamic viscosity.
Associated Implementation#
The current implementation is provided through: