On the behaviour of numerical schemes in the low Mach number regime PDF

On the behaviour of numerical schemes in the low Mach number regime PDF or paste a DOI name into the text box. A novel deep learning framework to forecast electricity prices is proposed.


Författare: Felix Rieper.
Computational fluid dynamics (CFD) was for a long
time rigidly divided between simulating compressible
and incompressible flows, but a variety of important
flow phenomena like atmospheric flows are
quasi-incompressible with significant density
varations. Because of the good properties of schemes
for compressible flows, one asks the question: can
these methods cope with low Mach numbers? For
decades the answer was somewhat fuzzy: Yes, in
principle, but with deteriorating results for
decreasing Mach numbers.
In this book we shed light on this phenomenon,
showing that there are two sources of error: The
flux-function and the grid cell geometry. In the
first part we demonstrate that flux-functions fall
into two classes: one resolves all characteristic
waves of the Riemann problem while the other becomes
more and more diffusive for lower Mach numbers. In
the second part, we present an intriguing new result:
first-order upwind schemes can manage small Mach
number flows but only if the grid is made up of
triangular cells. Using graph theory we show that the
number of degrees of freedom for the velocity field
on cells with more than three edges is reduced to zero.

The framework leads to accuracy improvements that are statistically significant. The largest benchmark to date in electricity price forecasting is presented. 27 state-of-the-art methods for predicting electricity prices are compared. Machine learning models are shown to, in general, outperform statistical methods.

While many predictive models have been already proposed to perform this task, the area of deep learning algorithms remains yet unexplored. To create, disseminate and apply the state-of-the-art technologies and practices to societal problems. To build top of the line faculty through appropriate human resource policies and to create effective interface with industries, business and community to make education responsive to changes. To promote a cosmopolitan outlook among the students and faculty and to develop a sense of national integration. To deliver comprehensive education in Mechanical Engineering to ensure that the graduates attain the core competency to be successful in industry or excel in higher studies in any of the following fields: Thermal Engineering, Mechanical Design, and Manufacturing Science and Technology.