NeumannBoundaryUnitNormal

NeumannBoundaryUnitNormal[{x,y,}]

represents an outward-pointing unit normal vector at the point on the boundary of a filled region.

Details

Examples

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Basic Examples  (2)

Set up a symbolic electric current density boundary condition with a non-surface normal current density:

Specify a differential equation operator :

Specify a region:

On the left, a NeumannValue is set up. The default Neumann boundary integrand for this equation is . To model a boundary integrand of the form , a NeumannValue is set up:

Visualize the solution:

Scope  (5)

For nonconservative mass transport, boundary conditions like MassImpermeableBoundaryValue can produce NeumannBoundaryUnitNormal. Set up an impermeable boundary condition for a nonconservative model:

NeumannBoundaryUnitNormal can be used in NIntegrate to compute the flux through a boundary. Solve a Poisson equation on a unit Disk:

Visualize the solution:

Compute the total flux through the boundary of the region through the boundary region:

Compute the total flux through the boundary of a subregion:

Specify a time-dependent differential equation operator :

Specify a region:

On the left, a NeumannValue is set up. The default Neumann boundary integrand for this equation is . To model a boundary integrand of the form , a NeumannValue is set up:

Use a Neumann 0 boundary condition and solve the equation again:

Inspect how the solutions start to differ over time:

Create a tangential for a NeumannValue:

Make use of an Indexed component, the component, of a NeumannBoundaryUnitNormal to compute a NeumannValue:

Applications  (1)

The AcousticRadiationValue makes use of a NeumannBoundaryUnitNormal to automatically compute the sound direction vector. Define model variables vars for a frequency domain acoustic pressure field with model parameters pars:

Set up the equation with a radiation boundary at the left end and an acoustic absorbing boundary at the right end:

Set up the parametric solver:

Convert the solution to the time domain and visualize the solution in the frequency domain at various frequencies :

Properties & Relations  (1)

The boundary unit normal is computed by solving a Poisson equation over the region and specifying 0 Dirichlet conditions. Compute a Poisson equation over a unit Disk:

Compute the normalized gradient of the potential:

Visualize the unit normal:

Wolfram Research (2025), NeumannBoundaryUnitNormal, Wolfram Language function, https://reference.wolfram.com/language/ref/NeumannBoundaryUnitNormal.html.

Text

Wolfram Research (2025), NeumannBoundaryUnitNormal, Wolfram Language function, https://reference.wolfram.com/language/ref/NeumannBoundaryUnitNormal.html.

CMS

Wolfram Language. 2025. "NeumannBoundaryUnitNormal." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/NeumannBoundaryUnitNormal.html.

APA

Wolfram Language. (2025). NeumannBoundaryUnitNormal. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/NeumannBoundaryUnitNormal.html

BibTeX

@misc{reference.wolfram_2024_neumannboundaryunitnormal, author="Wolfram Research", title="{NeumannBoundaryUnitNormal}", year="2025", howpublished="\url{https://reference.wolfram.com/language/ref/NeumannBoundaryUnitNormal.html}", note=[Accessed: 20-January-2025 ]}

BibLaTeX

@online{reference.wolfram_2024_neumannboundaryunitnormal, organization={Wolfram Research}, title={NeumannBoundaryUnitNormal}, year={2025}, url={https://reference.wolfram.com/language/ref/NeumannBoundaryUnitNormal.html}, note=[Accessed: 20-January-2025 ]}