# /UPWM/SUPG (Obsolete)

Engine Keyword This describes the Streamline Upwind Petrov Galerkin formulation.

/UPWM/SUPG

fac

## Definitions

Field Content SI Unit Example
fac Scale factor applied on Petrov Galerkine weighting function.

Default = 1.00 (recommended value).

1. The streamline upwind Petrov-Galerkine (SUPG) is an optimal upwinding technique which acts only in the flow direction.
2. If this keyword is used, the usual upwind method for momentum advection is no longer used. As a consequence, the coefficient ${\eta }_{1}$ from /UPWIND (Obsolete) Starter is also not used.
3. The Galerkin (shape function φ) are modified to integrate the momentum convection term [(u - w). ∇]u, which leads to a Petrov Galerkin method using weight function W* such as:(1)
$W*=\phi +fac\frac{k\text{'}}{{\left(u-w\right)}^{2}}{u}_{j}\frac{\partial \phi }{\partial {x}_{j}}$

Where, k' is a function of the Reynolds number, material velocity and element length, and fac is a scale factor. fac = 1.00 is the standard value for SUPG formulation (recommended).

4. The /UPWM/SUPG and /UPWM/TG (Obsolete) options are available in 3D Euler, 3D ALE and 2D Euler, although they are not recommended in axisymmetric cases.
5. It is available for multi-material LAW51.
6. The upwinding technique is introduced to add numerical diffusion to the scheme which, otherwise is generally under-diffusive and thus unstable. The usual method is first: order accurate and strongly depends on the mesh aspect. In some cases (see examples below) the classical method might lead to locally erratic velocities with unsuitable meshes. SUPG method provides more accurate results, if the phenomenon is sensitive to mesh aspect. It is recommended to systematically activate it.
Modeling situation: A regular mesh is used although this phenomenon has spherical evolution. Result are obtained with multi-material LAW51.
Velocity Result - Classical UPWIND: Classical UPWIND method for momentum transportation is not suitable with spherical evolution and regular mesh.
Velocity Result - SUPG: SUPG method for momentum advection removes mesh sensitivity. It is no longer required to have a spherical mesh to model spherical phenomena.