ConservativeConvectionPDETerm[vars,α]
represents a conservative convection term 
with conservative convection coefficient 
and model variables vars.
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. - A symbolic conservative convection coefficient can be specified through a VectorSymbol. »
- 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 all close allBasic Examples (4)
Scope (10)
Define a symbolic conservative convection term:
Define a symbolic vector conservative convection term:
Define a stationary dependent convection term with a symbolic vector convection coefficient replaced:
Define a time-dependent convection term with a symbolic vector convection coefficient replaced:
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 time-independent 2D 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)
A conservative convection term with a 0-flow velocity field evaluates to 0:
A symbolic convection coefficient needs to be of sufficient length:
The way to specify the symbolic vector convection coefficient is through a VectorSymbol:
Substitute a VectorSymbol with an actual value:
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 (updated 2025).
CMS
Wolfram Language. 2020. "ConservativeConvectionPDETerm." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2025. 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