MassImpermeableBoundaryValue
MassImpermeableBoundaryValue[pred,vars,pars]
represents a mass impermeable boundary condition for PDEs with predicate pred indicating where it applies, with model variables vars and global parameters pars.
MassImpermeableBoundaryValue[pred,vars,pars,lkey]
represents a mass impermeable boundary condition with local parameters specified in pars[lkey].
Details
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- MassImpermeableBoundaryValue specifies a boundary condition for MassTransportPDEComponent and is used as part of the modeling equation:
- MassImpermeableBoundaryValue is typically used to model a mass species impermeable boundary.
- MassImpermeableBoundaryValue models a boundary where there is no mass species flux across it with dependent variable
in [
], independent variables
in [
] and time variable
in [
].
- Stationary variables vars are vars={c[x1,…,xn],{x1,…,xn}}.
- Time-dependent variables vars are vars={c[t,x1,…,xn],t,{x1,…,xn}}.
- The non-conservative time-dependent mass transport model MassTransportPDEComponent is based on a convection-diffusion model with mass diffusivity
, mass convection velocity vector
, mass reaction rate
and mass source term
:
- The conservative time-dependent mass transport model MassTransportPDEComponent is based on a conservative convection-diffusion model given by:
- In the non-conservative form, MassImpermeableBoundaryValue with boundary unit normal
models:
- In the conservative form, MassImpermeableBoundaryValue models:
- A MassImpermeableBoundaryValue is the implicit default boundary condition for the conservative model form.
- Model parameters pars as specified for MassTransportPDEComponent.
- The following additional model parameters pars can be given:
-
parameter default symbol "BoundaryUnitNormal" Automatic "ModelForm" "NonConservative" - MassImpermeableBoundaryValue is a special case of MassFluxValue where the mass flux
is 0.
- MassImpermeableBoundaryValue evaluates to a NeumannValue.
- The boundary predicate pred can be specified as in NeumannValue.
- If the MassImpermeableBoundaryValue depends on parameters
that are specified in the association pars as …,keypi…,pivi,…], the parameters
are replaced with
.
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Examples
open allclose allBasic Examples (1)
Scope (3)
Define model variables vars for a transient acoustic pressure field with model parameters pars and a specific boundary condition parameter:
Define model variables vars for a transient acoustic pressure field with model parameters pars and multiple specific parameter boundary conditions:
The implicit default boundary condition changes depending on the model form. For a conservative model, an implicit Neumann 0 boundary condition is equivalent to specifying an impermeable boundary condition. For a non-conservative model, an implicit Neumann 0 boundary condition is equivalent to specifying an outflow boundary condition.
Considering this, for a constant velocity field, both the conservative and non-conservative models return the same result. A comparison between the conservative and non-conservative fields are conducted based on the following models:
Set up the mass transport model variables :
Specify model parameters species diffusivity and fluid flow velocity
:
Set up a species concentration source of 0.2 length at the center of the left surface:
Set up an outflow flux of
on the top and bottom surfaces:
Specify impermeable boundary conditions on all other sides:
Since the default boundary condition for a conservative model is an impermeable boundary, an impermeable boundary condition is added to the non-conservative model.
Text
Wolfram Research (2020), MassImpermeableBoundaryValue, Wolfram Language function, https://reference.wolfram.com/language/ref/MassImpermeableBoundaryValue.html.
CMS
Wolfram Language. 2020. "MassImpermeableBoundaryValue." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/MassImpermeableBoundaryValue.html.
APA
Wolfram Language. (2020). MassImpermeableBoundaryValue. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MassImpermeableBoundaryValue.html