Scale-Resolving Simulations with a Low-Dissipation Low-Dispersion Second-Order Scheme for Unstructured Flow Solvers

AIAA Journal ◽  
2016 ◽  
Vol 54 (10) ◽  
pp. 2972-2987 ◽  
Author(s):  
Axel Probst ◽  
Johannes Löwe ◽  
Silvia Reuß ◽  
Tobias Knopp ◽  
Roland Kessler
Keyword(s):  
Second Order ◽  
Low Dissipation ◽  
Order Scheme ◽  
Low Dispersion

Low-Dissipation Low-Dispersion Second-Order Scheme for Unstructured Finite Volume Flow Solvers

AIAA Journal ◽  
2016 ◽  
Vol 54 (10) ◽  
pp. 2961-2971 ◽  
Author(s):  
Johannes Löwe ◽  
Axel Probst ◽  
Tobias Knopp ◽  
Roland Kessler
Keyword(s):  
Finite Volume ◽  
Second Order ◽  
Volume Flow ◽  
Low Dissipation ◽  
Order Scheme ◽  
Low Dispersion

Low-dissipation low-dispersion explicit Taylor-Galerkin schemes from the Runge-Kutta kernels

2018 ◽  
Vol 17 (1-2) ◽  
pp. 88-113
Author(s):  
Mostafa Najafiyazdi ◽  
Luc Mongeau ◽  
Siva Nadarajah
Keyword(s):  
Time Integration ◽  
Second Order ◽  
Order Of Accuracy ◽  
Galerkin Scheme ◽  
Integration Schemes ◽  
Low Dissipation ◽  
Multi Stage ◽  
Time Integration Schemes ◽  
Runge Kutta ◽  
Low Dispersion

A multi-stage approach was adopted to investigate similarities and differences between the explicit Taylor-Galerkin and the explicit Runge-Kutta time integration schemes. It was found that the substitution of some, but not all, of second-order temporal derivatives in a Taylor-Galerkin scheme by additional stages makes it analogous to a Runge-Kutta scheme while preserving its original dissipative property for node-to-node oscillations. The substitution of all second-order temporal derivatives transforms Taylor-Galerkin schemes into Runge-Kutta schemes with zero attenuation at the grid cut-off. The application of this approach to an existing two-stage Taylor-Galerkin scheme yields a low-dissipation low-dispersion Taylor-Galerkin formulation. Two one-dimensional benchmarks were simulated to study the performance of this new scheme. The reverse process yields a general approach for transforming m-stage Runge-Kutta schemes into ( m−1)-stage Taylor-Galerkin schemes while preserving the same order of accuracy. The dissipation and dispersion properties for several new Taylor-Galerkin schemes were compared to those of their corresponding Runge-Kutta form.

scholarly journals Beyond second-order convergence in simulations of magnetized binary neutron stars with realistic microphysics

2019 ◽  
Vol 490 (3) ◽  
pp. 3588-3600 ◽  
Author(s):  
E R Most ◽  
L Jens Papenfort ◽  
L Rezzolla
Keyword(s):  
Neutron Stars ◽  
Fourth Order ◽  
Finite Temperature ◽  
Equations Of State ◽  
Magnetic Energy ◽  
Second Order ◽  
Conservative Finite Difference Scheme ◽  
Order Scheme ◽  
Convergence Orders ◽  
The Impact

ABSTRACT We investigate the impact of using high-order numerical methods to study the merger of magnetized neutron stars with finite-temperature microphysics and neutrino cooling in full general relativity. By implementing a fourth-order accurate conservative finite-difference scheme we model the inspiral together with the early post-merger and highlight the differences to traditional second-order approaches at the various stages of the simulation. We find that even for finite-temperature equations of state, convergence orders higher than second order can be achieved in the inspiral and post-merger for the gravitational-wave phase. We further demonstrate that the second-order scheme overestimates the amount of proton-rich shock-heated ejecta, which can have an impact on the modelling of the dynamical part of the kilonova emission. Finally, we show that already at low resolution the growth rate of the magnetic energy is consistently resolved by using a fourth-order scheme.

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