18 research outputs found
Computation of isotopisms of algebras over finite fields by means of graph invariants
In this paper we define a pair of faithful functors that map isomorphic and
isotopic finite-dimensional algebras over finite fields to isomorphic graphs.
These functors reduce the cost of computation that is usually required
to determine whether two algebras are isomorphic. In order to illustrate
their efficiency, we determine explicitly the classification of two- and threedimensional partial quasigroup rings
Industry-relevant implicit large-eddy simulation of a high-performance road car via spectral/HP element methods
This is the author accepted manuscript. The final version is available from the Society for Industrial and Applied Mathematics via the DOI in this recordWe present a successful deployment of high-fidelity Large-Eddy Simulation (LES)
technologies based on spectral/hp element methods to industrial flow problems, which are characterized by high Reynolds numbers and complex geometries. In particular, we describe the numerical
methods, software development and steps that were required to perform the implicit LES of a real
automotive car, namely the Elemental Rp1 model. To the best of the authors’ knowledge, this simulation represents the first high-order accurate transient LES of an entire real car geometry. Moreover,
this constitutes a key milestone towards considerably expanding the computational design envelope
currently allowed in industry, where steady-state modelling remains the standard. To this end, a
number of novel developments had to be made in order to overcome obstacles in mesh generation
and solver technology to achieve this simulation, which we detail in this paper. The main objective
is to present to the industrial and applied mathematics community, a viable pathway to translate
academic developments into industrial tools, that can substantially advance the analysis and design
capabilities of high-end engineering stakeholders. The novel developments and results were achieved
using the academic-driven open-source framework Nektar++.Engineering and Physical Sciences Research Council (EPSRC)European Union Horizon 2020Imperial College High Performance Computing ServiceNational University of SingaporeAirbu