Generalized Split-Explicit Runge–Kutta Methods for the Compressible Euler Equations

Knoth, Oswald; Wensch, Joerg

doi:10.1175/mwr-d-13-00068.1

Cited by 24 publications

(20 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It solves the three-dimensional, fully compressible Euler equations. Different time integration schemes are available, e.g., a split-explicit Runge-Kutta scheme (Knoth and Wensch, 2014) or an implicit Rosenbrock-type method. In the present study, ASAM is deployed as a LES model, for which part of the turbulent motion is resolved directly and the remaining part is parameterized by a subgrid-scale model.…”

Section: Use Of Les To Resolve Fire Dynamicsmentioning

confidence: 99%

Wildfires as a source of airborne mineral dust – revisiting a conceptual model using large-eddy simulation (LES)

Wagner¹,

Jähn²,

Schepanski³

2018

Atmos. Chem. Phys.

View full text Add to dashboard Cite

Abstract. Airborne mineral dust is a key player in the Earth system and shows manifold impacts on atmospheric properties such as the radiation budget and cloud microphysics. Investigations of smoke plumes originating from wildfires found significant fractions of mineral dust within these plumes – most likely raised by strong, turbulent fire-related winds. This study presents and revisits a conceptual model describing the emission of mineral dust particles during wildfires. This is achieved by means of high-resolution large-eddy simulation (LES), conducted with the All Scale Atmospheric Model (ASAM). The impact of (a) different fire properties representing idealized grassland and shrubland fires, (b) different ambient wind conditions modulated by the fire's energy flux, and (c) the wind's capability to mobilize mineral dust particles was investigated. Results from this study illustrate that the energy release of the fire leads to a significant increase in near-surface wind speed, which consequently enhances the dust uplift potential. This is in particular the case within the fire area where vegetation can be assumed to be widely removed and uncovered soil is prone to wind erosion. The dust uplift potential is very sensitive to fire properties, such as fire size, shape, and intensity, but also depends on the ambient wind velocity. Although measurements already showed the importance of wildfires for dust emissions, pyro-convection is so far neglected as a dust emission process in atmosphere–aerosol models. The results presented in this study can be seen as the first step towards a systematic parameterization representing the connection between typical fire properties and related dust emissions.

show abstract

Section: Use Of Les To Resolve Fire Dynamicsmentioning

confidence: 99%

Wildfires as a source of airborne mineral dust – revisiting a conceptual model using large-eddy simulation (LES)

Wagner¹,

Jähn²,

Schepanski³

2018

Atmos. Chem. Phys.

View full text Add to dashboard Cite

show abstract

“…see [5]. The critical parameters are the background velocity U and the speed of sound c. A spatial discretization on a staggered grid with upwind differencing for the advective (=slow) terms and symmetric differencing for the sound (=fast) terms results in an ordinary differential equation.…”

Section: The Methodsmentioning

confidence: 99%

TVD‐based Finite Volume Methods for Sound‐Advection‐Buyancy Systems

Knoth

Naumann²,

Wensch³

2014

Proc Appl Math and Mech

Self Cite

View full text Add to dashboard Cite

Split-explicit Runge-Kutta methods provide an efficient integration procedure for hyperbolic systems with coupled slow and fast wave phenomena. They are generalized to multirate infinitesimal step methods (MIS) in order to develop an order to provide order conditions and to establish stability properties. The construction of MIS methods is based on an underlying Runge-Kutta method. This method is choosen to be total variation diminishing (TVD) to improve the stability properties of the method. Here, the maximum Courant number is improved by a factor of 4.

show abstract

“…In recent years, several splitting methods were developed. Amongst them are the RK3 [1], the multirate infinitesimal step methods (MIS) [2] and multirate infinitesimal step PEER methods (MIS-PEER) [3]. Whereas the first two methods base on Runge-Kutta method, the latter one base on two step explicit PEER methods.…”

Section: Introductionmentioning

confidence: 99%

Multirate finite step methods with varying step sizes

Naumann

Wensch

2017

Proc Appl Math and Mech

View full text Add to dashboard Cite

Many partial differential equations consist of slow and fast scales. Often, the right hand side of semidiscretized PDEs can be split additively in corresponding fast and slow parts. Many methods utilise the additive splitting of these equations, like generalized additive Runge-Kutta (GARK) methods or multirate infinitesimal step methods. The latter one treat the slow part with macro step sizes, whereas the fast part is integrated a ODE solver. The corresponding order conditions assume the exact solution of the auxiliary ODE, i.e. assume an infinite number of small steps. We extend the MIS approach by fixing the number of steps, which leads to the multirate finite steps (MFS) method. The order conditions are derived, such that the order is independent in the number of small steps in each stage. Finally, we confirm the theoretical results by numerical experiments.

show abstract

Generalized Split-Explicit Runge–Kutta Methods for the Compressible Euler Equations

Cited by 24 publications

References 12 publications

Wildfires as a source of airborne mineral dust – revisiting a conceptual model using large-eddy simulation (LES)

Wildfires as a source of airborne mineral dust – revisiting a conceptual model using large-eddy simulation (LES)

TVD‐based Finite Volume Methods for Sound‐Advection‐Buyancy Systems

Multirate finite step methods with varying step sizes

Contact Info

Product

Resources

About