Mixed Mesh Finite Volume Method for 1D Hyperbolic Systems with Application to Plug-flow Heat Exchangers

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F21%3A00338034" target="_blank" >RIV/68407700:21230/21:00338034 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/68407700:21720/21:00338034

Výsledek na webu

<a href="https://doi.org/10.3390/math9202609" target="_blank" >https://doi.org/10.3390/math9202609</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/math9202609" target="_blank" >10.3390/math9202609</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Mixed Mesh Finite Volume Method for 1D Hyperbolic Systems with Application to Plug-flow Heat Exchangers

Popis výsledku v původním jazyce

We present a finite volume method formulated on a mixed Eulerian-Lagrangian mesh for highly advective 1D hyperbolic systems altogether with its application to plug-flow heat exchanger modeling/simulation. Advection of sharp moving fronts is an important problem in fluid dynamics, and even a simple transport equation cannot be solved precisely by having a finite number of nodes/elements/volumes. Finite volume methods are known to introduce numerical diffusion, and there exist a wide variety of schemes to minimize its occurrence; the most recent being adaptive grid methods such as moving mesh methods or adaptive mesh refinement methods. We present a solution method for a class of hyperbolic systems with one nonzero time-dependent characteristic velocity. This property allows us to rigorously define a finite volume method on a grid that is continuously moving by the characteristic velocity (Lagrangian grid) along a static Eulerian grid. The advective flux of the flowing field is, by this approach, removed from cell-to-cell interactions, and the ability to advect sharp fronts is therefore enhanced. The price to pay is a fixed velocity-dependent time sampling and a time delay in the solution. For these reasons, the method is best suited for systems with a dominating advection component. We illustrate the method’s properties on an illustrative advection-decay equation example and a 1D plug flow heat exchanger. Such heat exchanger model can then serve as a convection-accurate dynamic model in estimation and control algorithms for which it was developed.

Název v anglickém jazyce

Mixed Mesh Finite Volume Method for 1D Hyperbolic Systems with Application to Plug-flow Heat Exchangers

Popis výsledku anglicky

We present a finite volume method formulated on a mixed Eulerian-Lagrangian mesh for highly advective 1D hyperbolic systems altogether with its application to plug-flow heat exchanger modeling/simulation. Advection of sharp moving fronts is an important problem in fluid dynamics, and even a simple transport equation cannot be solved precisely by having a finite number of nodes/elements/volumes. Finite volume methods are known to introduce numerical diffusion, and there exist a wide variety of schemes to minimize its occurrence; the most recent being adaptive grid methods such as moving mesh methods or adaptive mesh refinement methods. We present a solution method for a class of hyperbolic systems with one nonzero time-dependent characteristic velocity. This property allows us to rigorously define a finite volume method on a grid that is continuously moving by the characteristic velocity (Lagrangian grid) along a static Eulerian grid. The advective flux of the flowing field is, by this approach, removed from cell-to-cell interactions, and the ability to advect sharp fronts is therefore enhanced. The price to pay is a fixed velocity-dependent time sampling and a time delay in the solution. For these reasons, the method is best suited for systems with a dominating advection component. We illustrate the method’s properties on an illustrative advection-decay equation example and a 1D plug flow heat exchanger. Such heat exchanger model can then serve as a convection-accurate dynamic model in estimation and control algorithms for which it was developed.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/TK01020024" target="_blank" >TK01020024: Hydronics 4.0</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2021

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Mathematics

ISSN

2227-7390

e-ISSN

2227-7390

Svazek periodika

9

Číslo periodika v rámci svazku

20

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

18

Strana od-do

—

Kód UT WoS článku

000714905500001

EID výsledku v databázi Scopus

2-s2.0-85117504751