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

Examples

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Basic Examples  (1)

Set up an impermeable boundary condition for a conservative model:

Set up an impermeable boundary condition for a non-conservative model:

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:

del .(-d del c(x,y))+v^->.del c(x,y)^(︷^( non-conservative mass transport model )) =|_(Gamma_(y=0, y=10))q(x,y)^(︷^( mass flux value ))

del .(-d del c(x,y))+del v^->.c(x,y)^(︷^( conservative mass transport model )) =|_(Gamma_(y=0, y=10))q(x,y)^(︷^( mass flux value ))

Set up the mass transport model variables vars:

Set up a rectangular domain:

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.

Set up the equation:

Solve the PDEs:

Visualize the differences in the solutions:

Wolfram Research (2020), MassImpermeableBoundaryValue, Wolfram Language function, https://reference.wolfram.com/language/ref/MassImpermeableBoundaryValue.html.

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

BibTeX

@misc{reference.wolfram_2024_massimpermeableboundaryvalue, author="Wolfram Research", title="{MassImpermeableBoundaryValue}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/MassImpermeableBoundaryValue.html}", note=[Accessed: 26-December-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_massimpermeableboundaryvalue, organization={Wolfram Research}, title={MassImpermeableBoundaryValue}, year={2020}, url={https://reference.wolfram.com/language/ref/MassImpermeableBoundaryValue.html}, note=[Accessed: 26-December-2024 ]}