%27.svg){kind=icon}
.ModelicaReference.Operators.'spatialDistribution()' .ModelicaReference.Operators.'spatialDistribution()'The operator spatialDistribution allows the infinite-dimensional problem below to be solved efficiently with good accuracy
where
z(x, t) is the transported quantity,
x is the normalized spatial coordinate (0.0 ≤
x ≤ 1.0), t is the time,
v(t) = der(x) is the normalized transport
velocity and the boundary conditions are set at either
x = 0.0 or x = 1.0, depending on the sign
of the velocity.
(out0, out1) = spatialDistribution(in0, in1, x, positiveVelocity,
initialPoints = {0.0, 1.0},
initialValues = {0.0, 0.0});
Many applications involve the modelling of variable-speed
transport of properties. One option to model this
infinite-dimensional system is to approximate it by an ODE, but
this requires a large number of state variables and might introduce
either numerical diffusion or numerical oscillations. Another
option is to use a built-in operator that keeps track of the
spatial distribution of z(x,t), by suitable sampling,
interpolation, and shifting of the stored distribution. In this
case, the internal state of the operator is hidden from the ODE
solver.
See Section 3.7.2.2 of the Modelica Language Specification 3.4 for a more in-depth description and elaborate example.