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Abstract:
Many flows relevant for climate research, weather forecasting, heating, ventilation,
air-conditioning (HVAC), and fire safety are characterized by relatively
small velocities compared to the speed of sound. The efficient computation of
such low Mach number flows requires computational methods that avoid the
Courant-Friedrich-Lewy time step restriction, based on the speed of sound. An
essential issue in the context meterological flow modelling, as investigated at
the Potsdam Institute for Climate Impact Research, is the construction of ef-
ficient numerical schemes for such flows that are in conservation form with
respect to all physically conserved quantities, i.e., mass, momentum, and energy.
Extending initial developments by Klein et. al [9, 13, 15, 19, 20], a new
scheme for such flows is currently under development which accounts for flows
in three space dimensions, is fully conservative, with second order accuracy
and covers the entire regime 0 <= M <= 1.
To transfer this scheme to practical applications, the author has created the
programm code MOLOCH. This technical report collects the background theory
of the scheme and describes the current state of its implementation. The code
is based on a finite-volume method using a cartesian grid. Currently, the scheme
is limited to Zero-Mach number.
The first four chapters describe the mathematical background of the scheme.
After a short presentation of the underlying set of equations, the result of a
one-scale asymptotic analysis is discussed to elucidate the main problems in
the context of constructing numerical simulation schemes, and to motivate the
construction of the method.
Chapter 5 describes the details of the numerical technique and provides additional
information regarding the discretization and the implementation of boundary
conditions.
Chapter 6 describes the implementation of gravitational forces, necessary
to run the falling droplet test case, which will be described in Chapter 7. An
empirical convergence study confirms the predicted second order accuracy of
the implemented scheme.
Current work in progress aims at extending the scheme presented here to
the meteorologically important class anelastic, instead of incompressible, flow
models. The computational code structure as presented here will transfer to
these applications without change.
