ICOSAHOM 2020
International Conference on Spectral and High Order Methods
12th  16th July 2021  Vienna, Austria
Conference Agenda
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Please note that all times are shown in the time zone of the conference. The current conference time is: 30th Nov 2022, 09:08:37pm CET

Session Overview 
Session  
MS 18a: 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  
12:00pm  12:30pm
HORSES3D: A HIGH ORDER DISCONTINUOUS GALERKIN SOLVER FOR FLOW SIMULATIONS AND MULTIPHYSICS APPLICATIONS ^{1}ETSIAEUPM (School of Aeronautics), Spain; ^{2}University of Cologne  Mathematical Institute; ^{3}San Diego State University We present the latest developments of our high order discontinuous Galerkin solvers: HORSES3D, capable of solving a range of flow applications including compressible, incompressible, turbulent (LES) and multiphase flows. We provide an overview of the different models implemented for turbulent flows (iLES, Smagorinsky, SVVSmagorinsky, WALE) [1, 7] and multiphase flows [24] (CahnHilliard). Additionally, we detail the capabilities to perform local padaption [56], implicit strategies and multigrid to advance the solution in time, efficiently. REERENCES [ 1 ]  J Manzanero, E Ferrer, G Rubio, E Valero, "Design of a Smagorinsky Spectral Vanishing Viscosity turbulence model for discontinuous Galerkin methods", Computers & Fluids, Vol 200, 2020 [ 2 ]  J Manzanero, G Rubio, DA Kopriva, E Ferrer, E Valero, "An entropy–stable discontinuous Galerkin approximation for the incompressible Navier–Stokes equations with variable density and artificial compressibility", Journal of Computational Physics, Vol 408, 2020 [ 3 ]  J Manzanero, G Rubio, DA Kopriva, E Ferrer, E Valero, "A freeenergy stable nodal discontinuous Galerkin approximation with summationbyparts property for the CahnHilliard equation", Journal of Computational Physics, Vol 403, 2020 [ 4 ]  J Manzanero, G Rubio, DA Kopriva, E Ferrer, E Valero, "Entropystable DG approximation with SBP property for the incompressible NavierStokes/CahnHilliard system", Accepted at Journal of Computational Physics 2020 [ 5 ]  AM RuedaRamirez, J Manzanero, E Ferrer, G Rubio, E Valero, "A pMultigrid Strategy with Anisotropic pAdaptation Based on Truncation Errors for HighOrder Discontinuous Galerkin Methods", Journal of Computational Physics, Vol 378, p 209233, 2019 [ 6 ]  AM RuedaRamirez, G Rubio, E Ferrer, E Valero, "Truncation Error Estimation in the pAnisotropic Discontinuous Galerkin Spectral Element Method", Journal of Scientific Computing, Vol 78(1), p 433466, 2019 [ 7 ]  E Ferrer, "An interior penalty stabilised incompressible Discontinuous Galerkin  Fourier solver for implicit Large Eddy Simulations", Journal of Computational Physics, Vol 348, p 754775, 2017 12:30pm  1:00pm
Implicit shock tracking for unsteady flows by the method of lines ^{1}Department of Mathematics, University of California, Berkeley, USA; ^{2}Mathematics Group, Lawrence Berkeley National Laboratory, USA; ^{3}Department of Aerospace and Mechanical Engineering, University of Notre Dame, USA We present the timedependent extension of our recently developed highorder implicit shock tracking (HOIST) framework for resolving discontinuous solutions of inviscid conservation laws. Central to the framework is an optimization problem which simultaneously computes a discontinuityaligned mesh and the corresponding highorder approximation to the flow, which provides nonlinear stabilization and a highorder approximation to the solution. The time discretization is based on method of lines and diagonally implicit RungeKutta (DIRK) methods, and we formulate and solve an optimization problem that produces a featurealigned mesh and solution at each RungeKutta stage of each timestep. A RankineHugoniot based prediction of the shock location together with a highorder untangling mesh smoothing procedure provides a highquality initial guess for the optimization problem at each time, which results in Newtonlike convergence of the sequential quadratic programming (SQP) optimization solver. This method is shown to deliver highly accurate solutions on coarse, highorder discretizations without nonlinear stabilization and recovers the design accuracy of the RungeKutta scheme. We demonstrate our framework using several inviscid unsteady conservation laws, and we verify that our method is able to recover the design order of accuracy of our time integrator in the presence of strong discontinuities. 1:00pm  1:30pm
Impact of wall modeling on kinetic energy stability for the compressible NavierStokes equations ^{1}Ocean in the Earth System, MaxPlanck Institute for Meteorolgy, Hamburg, Germany; ^{2}Faculty of Mechanical Engineering, Technion  Israel Institute of Technology, Haifa Israel; ^{3}Department of Mathematics, Computational Mathematics, Linköping University, SE581 83 Linköping, Sweden; ^{4}Department of Mathematics and Applied Mathematics, University of Johannesburg, PO Box 524, Auckland Park 2006, South Africa Affordable, high order simulations of turbulent flows on unstructured grids for very high Reynolds' number flows require wall models for efficiency. However, different wall models have different accuracy and stability properties. Here, we develop a kinetic energy stability estimate to investigate stability of wall model boundary conditions. Using this norm, two wall models are studied, a popular equilibrium stress wall model, which is found to be unstable and the dynamic slip wall model which is found to be stable. These results are extended to the discrete case using the Summationbyparts (SBP) property of the discontinuous Galerkin method. Numerical tests show that while the equilibrium stress wall model is accurate but unstable, the dynamic slip wall model is inaccurate but stable. 1:30pm  2:00pm
POD analysis of temporal flow patterns in different regimes ^{1}University of Malaga, Spain; ^{2}University of California, Davis Proper Orthogonal Decomposition (POD) has been used broadly in analyzing turbulent flows at high Reynolds numbers, such as flow in a pipe. However, there exists a lack of knowledge in analyzing some other regimes which contain interesting temporal behaviors. We present two study cases with completely different flow regimes showing the advantages of analyzing them using POD. First, we describe an application in creeping flow (very low Reynolds number) in NonNewtonian fluids. POD helps characterize the different bifurcations of the flow directly related to the movement of stagnation points of the problem. We have also proved the efficiency of this method to store data recovering 90% of the temporal evolution with only a few geometric modes (timeindependent) and some temporal modes, which are a single value for each time. Second, we analyze experimental data of a wing tip vortex at moderate Reynolds numbers. The possible attenuation of this kind of vortices is a key criterion for any airport design. By using POD, we were able to describe the vortex and isolate a mode representing the global attenuation of the vortex. 
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