ConservativeConvectionPDETerm
ConservativeConvectionPDETerm[vars,α]
represents a conservative convection term with conservative convection coefficient
and model variables vars.
ConservativeConvectionPDETerm[vars,α,pars]
uses model parameters pars.
Details



- Conservative convection is typically used to model transport due to a bulk movement and should be used when the divergence of convection velocity
is nonzero.
- Convection with a conservative convection coefficient
is the process of transport of the dependent variable
:
- ConservativeConvectionPDETerm returns a differential operators term to be used as a part of partial differential equations:
- ConservativeConvectionPDETerm can be used to model conservative 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 conservative convection term
in context with other PDE terms is given by:
- ConservativeConvectionPDETerm is similar to ConvectionPDETerm but affects the meaning of NeumannValue and has a coefficient
that is part of the divergence
.
- The conservative convection coefficient
has the following form:
-
{α1,…,αn} vector - For a system of PDEs with dependent variables {u1,…,um}, the conservative convection represents:
- The conservative convection term in context systems of PDE terms:
- The conservative 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 following parameters pars can be given:
-
parameter default symbol "RegionSymmetry" None - A possible choice for the parameter "RegionSymmetry" is "Axisymmetric".
- "Axisymmetric" region symmetry represents a truncated cylindrical coordinate system where the cylindrical coordinates are reduced by removing the angle variable as follows:
-
dimension reduction equation 1D 2D - All quantities that do not explicitly depend on the independent variables given are taken to have zero partial derivative.





Examples
open allclose allBasic Examples (3)Summary of the most common use cases
Scope (5)Survey of the scope of standard use cases
Define a 1D axisymmetric time-independent conservative convection term:
Apply Activate to the term:
Verify that the axisymmetric case is a consequence of using a truncated cylindrical coordinate system using the operators that compose the conservative convection term:
Define a 2D stationary conservative convection term:
Define a 2D axisymmetric time-independent conservative convection term:
Apply Activate to the term:
Verify that the axisymmetric case is a consequence of using a truncated cylindrical coordinate system using the operators that compose the conservative convection term:
Define a conservative convection term with multiple dependent variables:
Define an axisymmetric conservative convection term with multiple dependent variables:
Possible Issues (2)Common pitfalls and unexpected behavior
A conservative convection term with a 0-flow velocity field evaluates to 0:
A symbolic conservative convection coefficient is interpreted as a vector convection coefficient:
A subsequent substitution must account for that:
An alternative is to specify the symbolic convection coefficient as a vector:
Text
Wolfram Research (2020), ConservativeConvectionPDETerm, Wolfram Language function, https://reference.wolfram.com/language/ref/ConservativeConvectionPDETerm.html.
CMS
Wolfram Language. 2020. "ConservativeConvectionPDETerm." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ConservativeConvectionPDETerm.html.
APA
Wolfram Language. (2020). ConservativeConvectionPDETerm. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ConservativeConvectionPDETerm.html