# /ALE/SOLVER/FINT

Engine Keyword This option defines the numerical method for internal force integration. This is relevant only for brick element and the ALE legacy solver (momentum equation solved with FEM).

## Format

/ALE/SOLVER/FINT/`Iform`

## Definition

Field | Contents | SI Unit Example |
---|---|---|

Iform |
Integration method
(internal force for brick elements) flag.- = 0
- Set to 3.
- = 1
- Volume integration of the stress tensor using a shape function.
- = 2
- Surface integration for the hydrostatic stress tensor only.
- = 3 (Default)
- Surface integration for the stress tensor.
(Real) |

## Comments

- Momentum equation has
local form:$$\frac{\partial \rho u}{\partial t}+div\left(\rho uu\right)=div\left(\sigma \right)+\rho g$$
`Iform`is a flag defining the numerical method to compute $div\left(\sigma \right)$ when integrated over the cell with legacy solver (nodal velocities).`Iform`=1- ${F}_{\mathrm{int}}={\displaystyle {\int}_{\Omega}^{}div(\sigma )}dV$
`Iform`=2- ${F}_{\mathrm{int}}=\text{-}{\displaystyle {\int}_{\partial \Omega}^{}p}dS+{\displaystyle {\int}_{\Omega}^{}div(\sigma )}dV$
`Iform`=3- ${F}_{\mathrm{int}}={\displaystyle {\int}_{\partial \Omega}^{}\left(\text{-}pI+{\sigma}_{dev}\right)}dS$

For volume integration, shape functions are used to compute at node, N:

$${F}_{\mathrm{int}}^{iN}={\sigma}_{ik}{\frac{\partial {\Phi}_{N}}{\partial {x}_{k}}|}_{0}\left|\Omega \right|$$Where, $i=1,3$

The value ${\frac{\partial {\Phi}_{N}}{\partial {x}_{k}}|}_{0}$ is taken at the integration point. It is assumed that:

$$\frac{\partial {\Phi}_{N1}}{\partial {x}_{j}}=-\frac{\partial {\Phi}_{N7}}{\partial {x}_{j}}\text{};\text{}\frac{\partial {\Phi}_{N2}}{\partial {x}_{j}}=-\frac{\partial {\Phi}_{N8}}{\partial {x}_{j}}\text{};\text{}\frac{\partial {\Phi}_{N3}}{\partial {x}_{j}}=-\frac{\partial {\Phi}_{N5}}{\partial {x}_{j}}\text{};\text{}\frac{\partial {\Phi}_{N4}}{\partial {x}_{j}}=-\frac{\partial {\Phi}_{N6}}{\partial {x}_{j}}$$This assumption is exact for parallelepipedic shape only, which is why the new default value method is set to surface integration (

`Iform`=3).