<h3>Massively parallel non-matching grid simulations of fluid structure interaction problems</h3>
-In this tutorial we consider a mixing problem for laminar flows. Mixing
-problems are particularly hard to solve numerically, because they often involve
-a container (with fixed boundaries, and possibly complex geometries),
-represented by the domain $\Omega$, and one (or more) immersed and rotating
-impellers (represented by the domain $\Omega^{\text{imp}}$).
+In this tutorial we consider a mixing problem in the laminar flow regime.
+They occur in a wide range of applications ranging from chemical engineering to power
+generation (e.g. turbomachinery). Mixing problems are particularly hard to solve numerically,
+because they often involve a container (with fixed boundaries, and possibly
+complex geometries such as baffles), represented by the domain $\Omega$,
+and one (or more) immersed and rotating impellers (represented by the domain $\Omega^{\text{imp}}$).
The domain in which we would like to solve the flow equations is the (time
depedendent) difference between the two domains, namely:
(in which the fluid domain is smoothly deformed to follow the deformations
of the immersed solid) is not possible, unless only small times (i.e.,
small fluid domain deformations) are considered. If one wants to track the
-evolution of the flow across a few turns of the impellers, the resulting
+evolution of the flow across multiple rotations of the impellers, the resulting
deformed grid would simply be too distorted to be useful.
In this case, a viable alternative strategy would be to use non-matching
# that describes the function, rather than having to use its numeric value
# everywhere the constant appears. These values can be defined using this
# parameter, in the form `var1=value1, var2=value2, ...'.
- #
+ #
# A typical example would be to set this runtime parameter to
# `pi=3.1415926536' and then use `pi' in the expression of the actual
# formula. (That said, for convenience this class actually defines both
# `pi' and `Pi' by default, but you get the idea.)
- set Function constants =
+ set Function constants =
# The formula that denotes the function you want to evaluate for
# particular values of the independent variables. This expression may
# true, and to the third argument otherwise. For a full overview of
# possible expressions accepted see the documentation of the muparser
# library at http://muparser.beltoforion.de/.
- #
+ #
# If the function you are describing represents a vector-valued function
# with multiple components, then separate the expressions for individual
# components by a semicolon.
# that describes the function, rather than having to use its numeric value
# everywhere the constant appears. These values can be defined using this
# parameter, in the form `var1=value1, var2=value2, ...'.
- #
+ #
# A typical example would be to set this runtime parameter to
# `pi=3.1415926536' and then use `pi' in the expression of the actual
# formula. (That said, for convenience this class actually defines both
# `pi' and `Pi' by default, but you get the idea.)
- set Function constants =
+ set Function constants =
# The formula that denotes the function you want to evaluate for
# particular values of the independent variables. This expression may
# true, and to the third argument otherwise. For a full overview of
# possible expressions accepted see the documentation of the muparser
# library at http://muparser.beltoforion.de/.
- #
+ #
# If the function you are describing represents a vector-valued function
# with multiple components, then separate the expressions for individual
# components by a semicolon.
set Velocity degree = 2
set Viscosity = 1
subsection Angular velocity
- set Function constants =
+ set Function constants =
set Function expression = t < .500001 ? 5 : -5
set Variable names = x,y,t
end
set Refinement strategy = fixed_fraction
end
subsection Right hand side
- set Function constants =
+ set Function constants =
set Function expression = 0; 0; 0
set Variable names = x,y,t
end
set Velocity degree = 2
set Viscosity = 1
subsection Angular velocity
- set Function constants =
+ set Function constants =
set Function expression = t < .500001 ? 5 : -5
set Variable names = x,y,z,t
end
set Refinement strategy = fixed_fraction
end
subsection Right hand side
- set Function constants =
+ set Function constants =
set Function expression = 0; 0; 0; 0
set Variable names = x,y,z,t
end
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