Abstract: We present a new class of numerical techniques to
solve shallow water flows over dry areas including run-up. Many
recent investigations on wave run-up in coastal areas are based on
the well-known shallow water equations. Numerical simulations have
also performed to understand the effects of several factors on tsunami
wave impact and run-up in the presence of coastal areas. In all these
simulations the shallow water equations are solved in entire domain
including dry areas and special treatments are used for numerical
solution of singularities at these dry regions. In the present study we
propose a new method to deal with these difficulties by reformulating
the shallow water equations into a new system to be solved only in the
wetted domain. The system is obtained by a change in the coordinates
leading to a set of equations in a moving domain for which the
wet/dry interface is the reconstructed using the wave speed. To solve
the new system we present a finite volume method of Lax-Friedrich
type along with a modified method of characteristics. The method is
well-balanced and accurately resolves dam-break problems over dry
areas.
Abstract: A fast finite volume solver for multi-layered shallow
water flows with mass exchange and an erodible bed is developed.
This enables the user to solve a number of complex sediment-based
problems including (but not limited to), dam-break over an erodible
bed, recirculation currents and bed evolution as well as levy and
dyke failure. This research develops methodologies crucial to the
under-standing of multi-sediment fluvial mechanics and waterway
design. In this model mass exchange between the layers is allowed
and, in contrast to previous models, sediment and fluid are able
to transfer between layers. In the current study we use a two-step
finite volume method to avoid the solution of the Riemann problem.
Entrainment and deposition rates are calculated for the first time in
a model of this nature. In the first step the governing equations are
rewritten in a non-conservative form and the intermediate solutions
are calculated using the method of characteristics. In the second stage,
the numerical fluxes are reconstructed in conservative form and are
used to calculate a solution that satisfies the conservation property.
This method is found to be considerably faster than other comparative
finite volume methods, it also exhibits good shock capturing. For most
entrainment and deposition equations a bed level concentration factor
is used. This leads to inaccuracies in both near bed level concentration
and total scour. To account for diffusion, as no vertical velocities
are calculated, a capacity limited diffusion coefficient is used. The
additional advantage of this multilayer approach is that there is a
variation (from single layer models) in bottom layer fluid velocity:
this dramatically reduces erosion, which is often overestimated in
simulations of this nature using single layer flows. The model is
used to simulate a standard dam break. In the dam break simulation,
as expected, the number of fluid layers utilised creates variation in
the resultant bed profile, with more layers offering a higher deviation
in fluid velocity . These results showed a marked variation in erosion
profiles from standard models. The overall the model provides new
insight into the problems presented at minimal computational cost.
Abstract: Supersonic wind tunnel nozzles are generally capable of producing a constant Mach number flow in the test section of the wind tunnel. As a result, most of the supersonic vehicles are widely designed using steady state flow characteristics which may have errors while facing unsteady situations. This study aims to explore the possibility of varying the Mach number of the flow during wind tunnel operation. The nozzle walls are restricted to be inflexible for cooling near the throat due to high stagnation temperature requirement of the flow to simulate the conditions as experienced by the vehicle. Two simple independent mechanisms, rotation and translation of nozzle walls have been analyzed and the nozzle ranges have been optimized to vary the Mach number from Mach 2 to Mach 5 using minimum number of nozzles in the wind tunnel.
Abstract: This paper presents circuit models to analyze the
conducted susceptibility of multiconductor shielded cables in
frequency domains using Branin’s method, which is referred to as the
method of characteristics. These models, which can be used directly
in the time and frequency domains, take into account the presence of
both the transfer impedance and admittance. The conducted
susceptibility is studied by using an injection current on the cable
shield as the source. Two examples are studied; a coaxial shielded
cable and shielded cables with two parallel wires (i.e., twinax cables).
This shield has an asymmetry (one slot on the side). Results obtained
by these models are in good agreement with those obtained by other
methods.