MassSymmetryValue
MassSymmetryValue[pred,vars,pars]
represents a mass symmetry boundary condition for PDEs with predicate pred indicating where it applies, with model variables vars and global parameters pars.
MassSymmetryValue[pred,vars,pars,lkey]
represents a mass symmetry boundary condition with local parameters specified in pars[lkey].
Details
- MassSymmetryValue specifies a boundary condition for MassTransportPDEComponent and is used as part of the modeling equation:
- MassSymmetryValue is typically used to model a boundary with mirror symmetry along an axis.
- MassSymmetryValue models a boundary with mirror symmetry with dependent variable
in [![TemplateBox[{InterpretationBox[, 1], {"mol", , "/", , {"m", ^, 3}}, moles per meter cubed, {{(, "Moles", )}, /, {(, {"Meters", ^, 3}, )}}}, QuantityTF]](Files/MassSymmetryValue.en/4.png "TemplateBox[{InterpretationBox[, 1], {\"mol\", , \"/\", , {\"m\", ^, 3}}, moles per meter cubed, {{(, \"Moles\", )}, /, {(, {\"Meters\", ^, 3}, )}}}, QuantityTF]")
], independent variables 
in [![TemplateBox[{InterpretationBox[, 1], "m", meters, "Meters"}, QuantityTF]](Files/MassSymmetryValue.en/6.png "TemplateBox[{InterpretationBox[, 1], \"m\", meters, \"Meters\"}, QuantityTF]")
] and time variable 
in [![TemplateBox[{InterpretationBox[, 1], "s", seconds, "Seconds"}, QuantityTF]](Files/MassSymmetryValue.en/8.png "TemplateBox[{InterpretationBox[, 1], \"s\", seconds, \"Seconds\"}, QuantityTF]")
]. - 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:
- The normal flow velocity
on the symmetry boundary will remain at zero at all times. - Both in the conservative and non-conservative forms, MassSymmetryValue with boundary unit normal
models: - Model parameters pars as specified for MassTransportPDEComponent.
- The following additional model parameters pars can be given:
-
parameter default symbol "ModelForm" "NonConservative" 
- MassSymmetryValue is effectively the same as MassFluxValue with a heat flux of 0.
- The boundary predicate pred can be specified as in NeumannValue.
- If the MassSymmetryValue depends on parameters
that are specified in the association pars as …,keypi…,pivi,…, the parameters 
are replaced with 
.
Examples
open all close allBasic Examples (3)
Set up a mass symmetry boundary condition:
MassSymmetryValue[x ≥ 0, {c[t, x, y], t, {x, y}}, <||>]Set up a system of mass symmetry boundary conditions:
MassSymmetryValue[x ≥ 0, {{Subscript[c, 1][x], Subscript[c, 2][x]}, {x, y}}, <||>]Symmetry boundaries can be used to reduce the size of the geometry of the model. Set up a mass transport equation:
vars = {c[x, y], {x, y}};
pars = <|"DiffusionCoefficient" -> 1, "MassSource" -> 1|>;Set up and visualize a region:
Ω = RegionDifference[Rectangle[{-1, 0}, {1, 1}], Rectangle[{-1 / 2, 0}, {1 / 2, 1 / 2}]];
RegionPlot[Ω, AspectRatio -> Automatic]Solve and visualize the equation:
cfun = NDSolveValue[{MassTransportPDEComponent[vars, pars] == 0, MassConcentrationCondition[y == 0, vars, pars, <|"MassConcentration" -> 0|>]}, c[x, y], {x, y}∈Ω];
ContourPlot[cfun, {x, y}∈Ω]Set up a region about the symmetry axis at 
:
Ω = RegionDifference[Rectangle[{0, 0}, {1, 1}], Rectangle[{0, 0}, {1 / 2, 1 / 2}]];
Show[Graphics[{{Dashed, Thick, Gray, Line[{{0, -0.1}, {0, 1.1}}]}}], RegionPlot[Ω, AspectRatio -> Automatic]]Solve and visualize the equation with a symmetry boundary at 
:
cfun = NDSolveValue[{MassTransportPDEComponent[vars, pars] == MassSymmetryValue[x == 0, vars, pars], MassConcentrationCondition[y == 0, vars, pars, <|"MassConcentration" -> 0|>]}, c[x, y], {x, y}∈Ω];
ContourPlot[cfun, {x, y}∈Ω]Scope (2)
Set up a mass symmetry boundary condition in 3D:
MassSymmetryValue[x ≥ 0, {c[x, y, z], {x, y, z}}, <||>]Define model variables vars for a mass concentration with model parameters pars and a specific parameter boundary condition:
vars = {c[x, y], {x, y}};
pars = <|"DiffusionCoefficient" -> 1, "MassSource" -> 1, "BoundaryCondition1" -> <||>|>;Evaluate the boundary condition:
MassSymmetryValue[x == 1 / 5, vars, pars, "BoundaryCondition1"]Text
Wolfram Research (2020), MassSymmetryValue, Wolfram Language function, https://reference.wolfram.com/language/ref/MassSymmetryValue.html.
CMS
Wolfram Language. 2020. "MassSymmetryValue." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/MassSymmetryValue.html.
APA
Wolfram Language. (2020). MassSymmetryValue. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MassSymmetryValue.html