Návrh modelu proudění plynu
Title Alternative:Design of gas flow model
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Date
2007
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Publisher
Technická Univerzita v Liberci
Abstract
Tato práce se zabývá implementací a numerickým řešením úlohy vazkého izotermického proudění stlačitelné tekutiny pomocí metody konečných diferencí (FDM - Finite Difference Method) a metody konečných objemů (FVM - Finite Volume Method). Pro metodu konečných diferencí je navrženo explicitní a implicitní schéma a pro metodu konečných objemů je to explicitní Lax-Friedrichsovo schéma. Pro matematický popis proudění jsou použity Navier-Stokesova rovnice, která popisuje zákon zachování hybnosti vazké tekutiny, rovnice kontinuity, která vyjadřuje zákon zachování hmoty, a stavová rovnice plynu. Všechna schémata se porovnávají na navržených testovacích úlohách, na dvojdimenzionální obdélníkové oblasti bez překážek a jednou vstupní hranou, jednou výstupní hranou a dvěma nepropustnými hranami. V práci se porovnává vliv velikosti časového kroku, prostorového kroku a dynamické viskozity na stabilitu jednotlivých schémat.
The topic of this work is numerical solution and implementation of isothermal viscous compressible flow using the Finite Difference Method and Finite Volume Method. There are different schemes proposed for both methods - implicit and explicit scheme for the Finite Difference Method and the Lax-Friedrichs explicit scheme for the Finite Volume Method. There is a mathematical description of the flow, which is based on the following three equations: Navier-Stokes equation which represents the momentum conservation law, continuity equation which represents the mass conservation law and the gas state equation. All of those schemes are compared on testing problems. The flow is solved in a two-dimensional rectangular space without barriers. There are one inlet side and one outlet side in the area. Two other sides are impermeable. In this work, the effect of size of time and spatial discretization step and size of dynamic viscosity parameter on results of individual schemes is compared.
The topic of this work is numerical solution and implementation of isothermal viscous compressible flow using the Finite Difference Method and Finite Volume Method. There are different schemes proposed for both methods - implicit and explicit scheme for the Finite Difference Method and the Lax-Friedrichs explicit scheme for the Finite Volume Method. There is a mathematical description of the flow, which is based on the following three equations: Navier-Stokes equation which represents the momentum conservation law, continuity equation which represents the mass conservation law and the gas state equation. All of those schemes are compared on testing problems. The flow is solved in a two-dimensional rectangular space without barriers. There are one inlet side and one outlet side in the area. Two other sides are impermeable. In this work, the effect of size of time and spatial discretization step and size of dynamic viscosity parameter on results of individual schemes is compared.
Description
katedra: KMO; přílohy: 1 cd; rozsah: 55 s.
Subject(s)
metoda konečných diferencí, metoda konečných objemů, izotermické proudění, finite volume method, finite difference method, isothermal flow