This is post is going to be mainly the overview of various preprints that we submitted recently with my precious co-authors.
Let us start with my favourite topic - the water waves. With Didier Clamond we finalized our preprint on the brand new regularized shallow water (Airy-Saint-Venant) equations. The main idea is to suppress shock waves (i.e. replace them by smoother fronts) without adding any dissipation, any dispersion. We decided to call this type of modification as Hamiltonian regularization. More details can be found in our preprint:
- D. Clamond & D. Dutykh. Non-dispersive conservative regularisation of nonlinear shallow water and isothermal Euler equations, 20 pp., Submitted, 2017
A few days ago I delivered a colloquium talk on this topic at the Laboratoire de Mathématiques Raphaël Salem, University of Rouen. The slides can be downloaded here.
Last month with Valery Liapidevskii we finalized a work, which was started back in 2011 when Valery came to my university as invited Professor. This work is devoted to the modelling of turbidity (density) currents in general, and focuses especially on the determination of the front velocity. After so many years of collaboration, the article turned out to be quite long:
- V. Liapidevskii, D. Dutykh & M. Gisclon. On the modelling of shallow turbidity flows, 60 pp., Submitted, 2017
And as always, there is a number of new submissions on the building physics matters. First of all, we continued our researches on the identification and optimal experimental design:
- J. Berger, T. Busser, D. Dutykh & N. Mendes. On the estimation of sorption isotherm coefficients using the optimal experiment design approach, 32 pp., Submitted, 2017
This is already the third preprint in this direction. Moreover, we started a new research direction - the application of spectral methods to building physics. The spectral methods are not new. However, they seem to be essentially unknown in the building physics community. Moreover, they are so efficient that they can be seen as model reduction techniques. Two following preprints are devoted to this topic:
- S. Gasparin, J. Berger, D. Dutykh & N.Mendes. Spectral Methods - Part 1: A fast and accurate approach for solving nonlinear diffusive problems, 40 pp., Submitted, 2017
- S. Gasparin, J. Berger, D. Dutykh & N. Mendes. Spectral Methods - Part 2: A comparative study of reduced order models for moisture transfer diffusive problems, 36 pp., Submitted, 2017
It goes without saying that all preprints are freely available through HAL server. The links are provided above.