14.1.2 Defining Eulerian boundaries
Products: Abaqus/Explicit Abaqus/CAE
References
Overview
In an Eulerian analysis you can define independent inflow and outflow conditions at an Eulerian boundary. An Eulerian boundary condition:
can be used to control the flow of material into the Eulerian domain;
can be used to define a pressure field at the boundary of an Eulerian domain;
can be used to apply a nonreflecting boundary condition at the truncated artificial boundary to simulate an infinite domain; and
is associated with a surface defined on the Eulerian mesh boundary where inflow or outflow occurs.
Defining the Eulerian boundary
Eulerian boundaries must be defined at surfaces on the Eulerian mesh boundary. You cannot define multiple Eulerian boundaries at the same surface.
| Input File Usage: | *EULERIAN BOUNDARY surface name |
| Abaqus/CAE Usage: | Load module: Create Boundary Condition: Category: Other, Types for Selected Step: Eulerian boundary: select region |
Defining the inflow condition
You can use the inflow condition to control the flow of material into the Eulerian domain.
Free inflow
If no Eulerian boundary is defined, material can flow into the Eulerian domain freely; and the material content and the state of each inflow material are equal to that which presently exists within the element. If an Eulerian boundary is defined, free inflow is the default inflow condition.
| Input File Usage: | *EULERIAN BOUNDARY, INFLOW=FREE |
| Abaqus/CAE Usage: | Eulerian boundary condition editor: Flow type: Inflow, Inflow: Free |
No inflow
You can specify an Eulerian boundary where no inflow can occur—no material or void can flow into the Eulerian domain through the specified boundary. The normal component of the velocity is set to zero if the velocity is directed inward at the boundary, while the tangential component of the velocity remains unchanged.
| Input File Usage: | *EULERIAN BOUNDARY, INFLOW=NONE |
| Abaqus/CAE Usage: | Eulerian boundary condition editor: Flow type: Inflow, Inflow: None |
Void inflow
You can also specify a boundary through which inflow can occur but the influx volume contains only void. Due to the inflow of void, an Eulerian domain that is initially completely full of material might become partially full during the analysis.
| Input File Usage: | *EULERIAN BOUNDARY, INFLOW=VOID |
| Abaqus/CAE Usage: | Eulerian boundary condition editor: Flow type: Inflow, Inflow: Void |
Defining the outflow condition
The outflow condition can be used to simulate an unbounded domain by reducing reflection at the outflow boundary or to prescribe a pressure field at the boundary.
Free outflow
If no Eulerian boundary condition is specified, material can flow out of the Eulerian domain freely; and the material content and the state of each outflow material are equal to that which presently exists within the element. If an Eulerian boundary condition is defined, free outflow is the default behavior if the void inflow condition is specified at the same surface.
| Input File Usage: | *EULERIAN BOUNDARY, OUTFLOW=FREE |
| Abaqus/CAE Usage: | Eulerian boundary condition editor: Flow type: Outflow, Outflow: Free |
Nonreflecting outflow
A nonreflecting outflow condition can be used in boundary value problems defined in unbounded domains or problems in which the region of interest is small in size compared to the surrounding medium. Like the infinite element formulation described in “Using solid medium infinite elements in dynamic analyses” in “Infinite elements,” Section 28.3.1, the nonreflecting outflow condition introduces additional normal and shear tractions on the domain boundary that are proportional to the normal and shear components of the velocity of the boundary. These boundary damping constants are chosen to minimize the reflection of dilatational and shear wave energy back into the finite element mesh. This condition does not provide perfect transmission of energy out of the mesh except in the case of plane body waves impinging orthogonally on the boundary in an isotropic medium. However, it usually provides acceptable modeling for most practical cases. An exception is the case when significant material transport occurs through the boundary, in which case this condition is not suitable to be used.
| Input File Usage: | *EULERIAN BOUNDARY, OUTFLOW=NONREFLECTING |
| Abaqus/CAE Usage: | Eulerian boundary condition editor: Flow type: Outflow, Outflow: Nonreflecting |
Equilibrium outflow
Equilibrium outflow is another outflow condition that can effectively reduce spurious reflection at artificial outflow boundaries in unbounded domains. It is assumed that the stress is zero-order continuous across the element faces on the boundary. Traction is applied to these element faces to balance the nodal forces created by the stress in the boundary elements. This condition is usually applied at the outflow boundary where the pressure distribution is unknown.
| Input File Usage: | *EULERIAN BOUNDARY, OUTFLOW=NONUNIFORM PRESSURE |
| Abaqus/CAE Usage: | Eulerian boundary condition editor: Flow type: Outflow, Outflow: Equilibrium |
Zero-pressure outflow
It is common in flow problems to specify a zero pressure at the outlet of the flow. Since the normal traction on the boundary contains the contribution from both the pressure and the shear stress, the natural boundary condition, also known as the “do-nothing condition,” is not sufficient to provide such a condition if the shear behavior of the flow is also considered. The zero pressure outflow condition applies a traction that counteracts the shear contribution and, thus, generates a uniformly distributed pressure field on the boundary. You can apply a distributed surface load (see “Surface tractions and pressure loads” in “Distributed loads,” Section 34.4.3) on the same boundary to specify a nonzero pressure. This is the default outflow condition if the inflow condition is not specified.
| Input File Usage: | *EULERIAN BOUNDARY, OUTFLOW=ZERO PRESSURE |
| Abaqus/CAE Usage: | Eulerian boundary condition editor: Flow type: Outflow, Outflow: Zero pressure |
Using Eulerian boundaries in restart analyses
You can define a new Eulerian boundary in a restart analysis, but you cannot specify a void inflow condition at this boundary. In addition, you cannot change the inflow condition at an existing Eulerian boundary to the void inflow condition in a restart analysis.