ConvectionPDETerm
ConvectionPDETerm[vars,β]
represents a convection term with convection coefficient and model variables vars.
ConvectionPDETerm[vars,β,pars]
uses model parameters pars.
Details
- Convection terms are used in a number of domains such as thermodynamics, acoustics, structural mechanics and fluid dynamics.
- Convection is also known as advection.
- Convection with a convection coefficient is the process of transport of the dependent variable due to a bulk movement:
- ConvectionPDETerm returns a differential operators term to be used as a part of partial differential equations:
- ConvectionPDETerm can be used to model convection equations with dependent variable , independent variables and time variable .
- Stationary model variables vars are vars={u[x1,…,xn],{x1,…,xn}}.
- Time-dependent model variables vars are vars={u[t,x1,…,xn],{x1,…,xn}} or vars={u[t,x1,…,xn],t,{x1,…,xn}}.
- The convection term in context with other PDE terms is given by:
- During convection, the medium in which the convection happens is the transport mechanism, in contrast to diffusion where the medium remains stationary.
- The convection coefficient has the following form:
-
{β1,…,βn} vector - For a system of PDEs with dependent variables {u1,…,um}, the convection represents:
- The convection term in context systems of PDE terms:
- The convection coefficient is a tensor of rank 3 of the form where each submatrix is a vector of length that is specified in the same way as for a single dependent variable.
- The conservative convection coefficient can depend on time, space, parameters and the dependent variables.
- The coefficient does not affect the meaning of NeumannValue.
- All quantities that do not explicitly depend on the independent variables given are taken to have zero partial derivative.
- The ConservativeConvectionPDETerm is closely related.
Examples
open allclose allBasic Examples (4)
Scope (4)
Applications (3)
Use DiffusionPDETerm to model species diffusion under a dam. Set up the region:
Find the concentration of species under the dam. Construct the model:
Visualize the species concentration:
Extend a Stokes-flow model to a Navier–Stokes flow model. Define a Stokes-flow model:
Text
Wolfram Research (2020), ConvectionPDETerm, Wolfram Language function, https://reference.wolfram.com/language/ref/ConvectionPDETerm.html.
CMS
Wolfram Language. 2020. "ConvectionPDETerm." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ConvectionPDETerm.html.
APA
Wolfram Language. (2020). ConvectionPDETerm. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ConvectionPDETerm.html