ICOSAHOM 2020
International Conference on Spectral and High Order Methods
12th  16th July 2021  Vienna, Austria
Conference Agenda
Overview and details of the sessions of this conference. Please select a date or location to show only sessions at that day or location. Please select a single session for detailed view (with abstracts and downloads if available).
Please note that all times are shown in the time zone of the conference. The current conference time is: 10th Dec 2022, 11:01:26am CET

Session Overview 
Session  
MS 18b: Advances in high order methods for fluid dynamic
 
Session Abstract  
On approaching turbulence and geophysical domains, different scales appear in the problems (Aurnou et al, 2019). Small scales and large domains are difficult to reach with spectral methods because they are ill conditioned so that it is not possible to increase suitably the size of the expansions. A strategy to increase the size of the mesh avoiding the increase of the expansion are domain decomposition (DD) techniques (Quarteroni, 1999, 2002). Among them, the alternating Schwarz methods respect the original computation (Blayo, 2016; Xu, 2005). Herrero et al. applied this methodology to a stationary natural convection problem (Herrero, 2018). The method is expensive in time and unstable for some values of the parameters. A way of stabilization and optimization consists of using two levels of mesh in the alternating Schwarz method (Axelsson, 2019). Geophysical problems are studied using direct numerical simulations (GL Kooij et al. 2019, Curbelo et al. 2019). The study of instabilities requires the tracking of bifurcations varying parameters. These methods are based on the observation that varieties calculated by means of proper orthogonal decomposition (POD) from solutions at some values of the parameters also contain solutions to different values of the parameters. If the equations that govern the evolution of a system are dissipative, the behavior of the system for long times is contained in a finite dimensional inertial variety, which is often of a low dimension (Foias, 1988). Herrero et al. applied this type of methods for a RayleighBénard problem in a rectangular domain with reduced basis (Herrero, 2013) and taking as snapshots transient states of a temporal evolution towards a stationary solution or transient states of Newton's iteration for the treatment of nonlinearity for a fixed parameter value, managing to reproduce the diagram of bifurcations with very low computational cost (Pla, 2015). GutierrezCastillo et al. analyzed the use of POD for temporal flow patterns in nonnewtonian fluids.  
Presentations  
11:50am  12:20pm
An alternating Schwarz Method for a RayleighBénard Problem Universidad de CastillaLa Mancha, Spain A Schwarz domain decomposition numerical method for a stationary Rayleigh–Bénard convection problem is presented. The model equations are the stationary version of the incompressible Navier–Stokes equations coupled with a heat equation under Boussinesq approximation in a rectangular domain. A Newton method is used to deal with the nonlinearities. Each step in the Newton method is solved with an alternating Schwarz domain decomposition method. Their convergence properties are studied theoretically in a simplified domain. The numerical resolution of the problem confirms the theoretical results. The convergence rate is less than one when overlap is considered. Convergence is achieved for large values of the aspect ratio, which are inabordable for the standard Legendre collocation method. Other advantages of this methodology compared with standard methods are parallelization and high order. 12:20pm  12:50pm
Highorder fully wellbalanced LagrangeProjection scheme for shallow water equations Universidad de Cordoba, Spain We propose a novel strategy to define highorder fully wellbalanced LagrangeProjection finite volume solvers for balance laws. In particular, we focus on the 1D shallow water system. By fully wellbalanced, it is meant that the scheme is able to preserve stationary smooth solutions. As usual in LagrangeProjection schemes, we use the standard decomposition to naturally decouple the acoustic and transport phenomena. Such a decomposition proved to be useful and very efficient to deal with subsonic or near lowFroude number flows. In this case, the usual CFL time step limitation of Godunovtype schemes is indeed driven by the acoustic waves and can thus be very restrictive. The LagrangeProjection strategy allows to design a very natural implicitexplicit and large timestep schemes with a CFL restriction based on the (slow) transport waves and not on the (fast) acoustic waves. The proposed technique produces good results when applied to shallow water system. Note that, the LagrangeProjection scheme may be extended to other systems and applications such as bedload sediment transport, turbidity currents, Ripa system, etc. 12:50pm  1:20pm
Highorder spatial and temporal schemes suitable for polyhedral unstructured grids Instituto Superior Técnico, Portugal In a transient convectiondiffusion equation the global numerical error is the sum of the spatial and the temporal errors. With the finite volume method, the temporal term of the equation must be integrated in space with the same accuracy order as the convection and diffusion schemes. This novel approach considers an operator that converts pointwise values to mean ones, which enables the solution of unsteady highorder convectiondiffusion equations in the pointwise framework. One advantage of these schemes is the low number of contributions to the coefficient matrix when compared to the meanvalue counterpart. This becomes evident when extending eighthorder schemes to threedimensional cases. This novel operator uses only even cellcentered derivatives and cell’s even momentum of inertial. To reduce the number of required time steps, highorder backwards differentiation schemes are implemented leading to considerable time savings when using highorder spatial schemes. The numerical spatial error evolution with the solver runtime and the required memory is studied as an efficiency metrics of the implemented highorder schemes. Acknowledgement. The first author would like to acknowledge the current grant received by FCT – Portugal “Fundação para a Ciência e Tecnologia”, with the reference number 2020.07754.BD This work is a contribution from the research project HIBforMBP – “Highorder immersed boundary for moving body problems”, reference PTDC/EMEEME/32315/2017, which is financially supported by FCT  “Fundação para a Ciência e Tecnologia”  www.fct.pt . 
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