# Automatic Grid Computation

- 0 - J. Donea Grid Formulation: use keyword /DONEA
(NWALE =0 for version < 4.1)

- 1 - Average Displacement Formulation: use keyword /DISP
(NWALE =1 for version < 4.1)

- 2 - Nonlinear Spring Formulation: use keyword /SPRING
(NWALE =2 for version < 4.1)

## J. Donea Grid Formulation (/DONEA)

^{1}

^{2}computes grid velocity using:

- $1-\gamma \le \frac{w}{v}\le 1+\gamma $
- $N$
- Number of nodes connected to node I
- ${L}_{IJ}$
- Distance between node I and node J
- α, $\gamma $
- adimensional factors given in input

## Average Displacement Formulation (/DISP)

## Nonlinear Spring Formulation (/SPRING)

- $\text{\Delta}{T}_{0}$
- Typical time step (Must be greater than the time step of the current run.)
- $0<\gamma <1$
- Nonlinearity factor
- $\eta $
- Damping coefficient
- V
- Shear factor (stiffness ratio between diagonal springs and springs along connectivities)

This formulation is the best of the three, but it is the most computationally expensive.

^{1}Donea J., “An Arbitary Lagrangian-Eulerian finite element method for transient dynamic fluid-structure interactions”, Computer methods in applied mechanics, 1982.

^{2}Brooks A.N. and Hughes T.J.R., “Streamline Upwind /Petrov-Galerkin Formulations for Convection Dominated Flows with particular Emphasis on the Incompressible Navier-Stokes Equations”, Computer Methods in Applied Mechanics and Engineering, Vol. 32, 1982.