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: 1st Dec 2022, 08:29:37am CET

Session Overview 
Session  
MS 26a: High order multidimensional structure preserving methods
 
Session Abstract  
a rich phenomenology. Numerical methods originally developed in onedimensional situations require excessive grid refinement in order to capture multidimensional phenomena, such as vortices, differential constraints, stationary states and other structures. These structures are themselves mostly given as differential operators. For being efficient, it is not sufficient to merely use high order methods. They need to be equipped with structurepreserving properties. There is a qualitative difference in the results obtained by methods which do not preserve any structures and by those which preserve structures. This is true even if the structures in question are differential operators, and are preserved only as a discretization. Such methods achieve unprecedented accuracy on poorly resolved grids. This minisymposium shall bring together researchers dealing with structure preservation in different contexts and foster exchange on recent and trendsetting strategies to achieve this properties.  
Presentations  
12:00pm  12:30pm
Residual distribution schemes: Extensions to structure preserving schemes ^{1}Universität Zürich, Switzerland; ^{2}Politecnico di Milano; ^{3}Johannes Gutenberg University Hyperbolic conservation laws/balance laws contain several structural properties like entropy, angula momentum, preservation of kinetic energy, and more. Actually, it depends on the considered system. However, the numerical schemes should be constructed in a way to mimic these behaviors discretely and avoid to violate them. Recently, a lot of work has been done in the development and construction of such structure preserving schemes where one has to pay attention to several components. In this talk, we consider this topic in the context of residual distribution schemes. We present some extensions using correcton terms (cf. Ranocha's talk "Entropy Corrections and Related Methods" in MS02), focus on boundary operators in terms of entropy/energy stability, and the application of limiter strategies to guarantee the positivity of several physical quantities. 12:30pm  1:00pm
The Active Flux method for nonlinear conservation/balance laws MaxPlanckInstitute for Plasma Physics, Munich The talk focuses on the numerical solution of hyperbolic conservations laws (possibly endowed with a source term) using the Active Flux method. This method is an extension of the finite volume method. Instead of solving a Riemann Problem, the Active Flux method uses actively evolved point values along the cell boundary in order to compute the numerical flux. Early applications of the method were linear equations with an available exact solution operator, and Active Flux was shown to be structure preserving in such cases. For nonlinear PDEs or balance laws, exact evolution operators generally are unavailable. I will discuss strategies how sufficiently accurate approximate evolution operators can be designed which allow to make Active Flux structure preserving / wellbalanced for nonlinear problems. 1:00pm  1:30pm
On Kinetic Energy and Entropy Stable Moving Mesh DG Methods for the simulation of low Mach number turbulent flow ^{1}FriedrichSchillerUniversität Jena; ^{2}Universität Stuttgart; ^{3}Universität zu Köln The construction of discontinuous Galerkin (DG) methods for the compressible Euler or NavierStokes equations (NSE) includes the approximation of nonlinear flux terms in the volume integrals. The terms can lead to aliasing and stability issues in turbulence simulations with moderate Mach numbers, e.g. due to underresolution of vortical dominated structures typical in large eddy simulations (LES). The kinetic energy or entropy are elevated in smooth, but underresolved parts of the solution which are affected by aliasing. It is known that the kinetic energy is not a conserved quantity for compressible flows, but for small Mach numbers minor deviations from a constant progression should be expected. For this reason, in the simulation of under resolved turbulent flow it is desirable to use kinetic energy preserving (KEP) or entropy conservative (EC) DG methods for the Euler equations and kinetic energy dissipative (KED) or entropy stable (ES) DG methods for the NSE, since these methods include by construction a dealiasing mechanism. In this talk, our recently developed provably high order KEP and EC DG methods [1,2] on moving curved hexahedral meshes for the three dimensional Euler equations are presented. Then these methods are used to derive KED and ES moving mesh DG methods for the NSE. Moving mesh methods are of interest to represent specific physical features of the flow or in the context of radaptation which involves the redistribution of the mesh nodes in regions of rapid variation of the solution. The three dimensional TaylorGreen vortex is investigated to show and analyze numerically the theoretical findings and robustness of the developed moving mesh methods for turbulent vortex dominated flows. 1:30pm  2:00pm
TREFFTZ METHODS FOR TRANSPORT EQUATIONS Sorbonne University, France Trefftz methods can be used for high order numerical discretization of linear problems with increasing complexity. We address PN angular approximation of transport equations (linear Boltzman equations with stiff coefficients), often encountered for in neutron propagation and transfer equations. Indeed Trefftz methods provide a natural way to define numerical methods with genuine balance between the differential part and the relaxation part. These methods are naturally written in the context of Discontinuous Galerkin (DG) methods, and so are called Trefftz Discontinuous Galerkin (TDG) methods. We will report on the construction of the method and excellent behavior for boundary layers. It certain cases, the numerical accuracy of TDG just outperform more traditional polynomial based DG. New theoretical convergence estimates show the enhanced high order accuracy of TDG with respect to DG. 
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