7.14. Equation Specification

This section is referenced in the following other sections

Simulation Setup: Equation Specification

7.14.2. Additional Line Commands

7.14.2.1. Elasticity Formulation

Syntax: Elasticity Formulation = {PLANE STRESS | PLANE STRAIN}
Scope: Aria Region
Summary: Assigns the elasticity formulation type for two-dimensional problems involving the MESH and SOLID equations (see Conservation of Solid Momentum).

7.14.2.2. Pressure Stabilization

Syntax

Pressure Stabilization IS Type WITH SCALING = C

Scope

Aria Region

Summary

Prescribe a stabilization technique for solving Momentum and Continuity with equal order interpolation.

Description

Aria supports both PSPG (Pressure Stabilized Petrov-Galerkin) and PSPP (Pressure Stabilized Pressure Projection) stabilization techniques for solving the MOMENTUM and CONTINUITY equations with equal order interpolation.

Valid options for the Type specification are:

NO_STABILIZATION
PSPG_CONSTANT
PSPG_LOCAL
PSPG_GLOBAL
PSPP_CONSTANT

NO_STABILIZATION disables any stabilization.

PSPP_CONSTANT results in the recently developed stabilization technique of [53] and [54].

In the PSPG forms of stabilization, introduced by [55], terms from the momentum equation are added to the continuity equation scaled by a multiplier, $\alpha$ . The exact form of the multiplier depend on a global Reynolds number that is defined as

(7.1) $Re \equiv \frac{\density |\v| \langle h\rangle}{2 \viscosity}$

Here, $\density$ is the density, $\viscosity$ is the viscosity, $|\v|$ is a velocity scale and $\langle h\rangle$ is an element length scale. Armed with $Re$ , the stabilization multiplier $\alpha$ is defined in one of two ways.

(7.2) $\alpha \equiv \begin{cases} \frac{\tau \langle h\rangle^2}{12 \viscosity} & Re \le 3 \\ \frac{\tau \langle h\rangle}{2 \density |\v|} & Re > 3 \end{cases}$

NB: Currently, Aria always uses the low-Reynolds number form of $\alpha$ .

The PSPG_LOCAL method computes $|\v|$ and $\langle h\rangle$ within each element. The PSPG_GLOBAL method computes $|\v|$ and $\langle h\rangle$ as averages over all of the elements with the MOMENTUM equation defined. The PSPG_CONSTANT gives $|\v|$ and $\langle h\rangle$ a value of 1 (one) and just uses the scale factor.

Parameter	Value	Default
Type	See Description	–
C	real	–

7.14.2.3. Save Residuals

Syntax

Save Residuals = {OFF | BEFORE_BCS | AFTER_BCS}

Scope

Aria Region

Summary

Causes Aria to save the residuals to a field with the prefix residual->, e.g., residual->Temperature. This will be done for all fields (though we could make it a per-field option).

For the choice BEFORE_BCS the residuals will be saved at the point in the assembly process where the primary equations have been assembled but prior to the assembly of any boundary conditions or distinguishing conditions. For the choice of AFTER_BCS the residuals will be saved after all BCs and distinguishing conditions have been applied. The default, OFF, is to not save the residuals.

This feature is only applicable when using the NEWTON nonlinear solution strategy.

7.14.2.4. Integration Rule

Beta Capability

Non-default integration rules are not heavily tested and should be used with caution.

Syntax: Integration Rule for Block Name = Order
Scope: Aria Region
Summary: Overrides the default integration rule for the equations defined on Block Name.

Parameter	Value	Default
Block Name	string	–
Order	integer	–

7.14.2.5. Advection Velocity

Syntax: Advection Velocity for Equation Name = Vel
Scope: Aria Region
Summary: Defines the velocity model to be used for the equation Equation Name. Velocity model can be XFER or any other vector velocity model defined in the Region.

Parameter	Value	Default
Block Name	string	–
Vel	string	–