High-order numerical methods have been considered and implemented in order
to assess their applicability in a range of complex
ows centering on shockinduced
turbulent mixing. Speci cally, Weighted Essentially Non-Oscillatory
(WENO) variable reconstruction schemes of fth and ninth order accuracy
have been investigated within the context of a nite volume Godunov solver.
In addition to this there have been further numerical developments to assess
the HLLC Riemann solver and various quasi-conservative multi-component
models in conjunction with the high-order methods.
Understanding the physics of fundamental
ow instabilities and turbulence is
increasingly necessary to the development of a vast range of engineering applications
with relation to
uid dynamics. It is desirable to develop numerical
methods that possess su cient accuracy to capture the detail of such
ows
while remaining robust and viable in terms of cost.
The WENO schemes have been tested on a number of cases in comparison with
more traditional second-order MUSCL schemes. These include two and three
dimensional, single and multi mode Richtmyer-Meshkov instabilities with differing
initial perturbations, a cube of homogeneous decaying turbulence and
two hypersonic geometry cases were simulated. The results from this research
were consistent. The higher-order methods provided measurably greater resolution
of small scale
uctuations. By conducting grid convergence studies it
was seen that the e ect of the higher-order methods was comparable to the
e ect of increasing the number of grid points. The cost analysis repeatedly
showed that despite the additional cost of using a higher-order method they
were much better value as they could resolve
ow features on a signi cantly
coarser grid.
The high-order methods were not only validated for a range of
ow problems
but shown to o er great value for their additional cost; they could potentially
help advance understanding and development in a wide range of elds much
faster than is currently the case
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