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Time Adaptive Implicit Methods for Solving Initial Value Problems in CFD

Lindén, Ylva LU (2015) In Master's Theses in Mathematical Sciences FMN820 20141
Mathematics (Faculty of Engineering)
Abstract
In modeling unsteady compressible viscous flow problems with the compressible Navier-Stokes equations, time adaptive implicit methods are needed to solve the initial value problems that arise when discretizing the equations in accordance with the method of lines. The methods most used in industrial code today are a family of multistep methods called BDF-methods. Because BDF-methods with higher order than two are not A-stable, and thus do not fulfill necessary stability requirements for CFD-purposes, it is relevant to investigate possible alternatives. SDIRK and ESDIRK-methods are families of implicit Runge-Kutta methods, for which no bound on the order for A-stable schemes have been proven. This thesis uses two different flow problems for... (More)
In modeling unsteady compressible viscous flow problems with the compressible Navier-Stokes equations, time adaptive implicit methods are needed to solve the initial value problems that arise when discretizing the equations in accordance with the method of lines. The methods most used in industrial code today are a family of multistep methods called BDF-methods. Because BDF-methods with higher order than two are not A-stable, and thus do not fulfill necessary stability requirements for CFD-purposes, it is relevant to investigate possible alternatives. SDIRK and ESDIRK-methods are families of implicit Runge-Kutta methods, for which no bound on the order for A-stable schemes have been proven. This thesis uses two different flow problems for comparing a second order BDF-method implemented in SUNDIALS, to SDIRK and ESDIRK methods implemented in TEMPO, a code developed by the University of Kassel. (Less)
Popular Abstract
Fluid dynamics is a branch of physics that allows us to study the flow of fluids, i.e. liquids and gases, using differential equations. This has a large number of applications, in a wide variety of fields. It has been used to design the shape of the car you drive, the tap in your sink and the mouth piece to your blow drier as well as airplane wings and rockets. In Computational Fluid Dynamics (CFD), the solution to differential equations is approximated using computers and finding new ways to make the methods for obtaining these approximations more efficient is a constant work in progress. In this thesis I am comparing methods for solving these differential equations already used in industry today, to methods that for reasons presented in... (More)
Fluid dynamics is a branch of physics that allows us to study the flow of fluids, i.e. liquids and gases, using differential equations. This has a large number of applications, in a wide variety of fields. It has been used to design the shape of the car you drive, the tap in your sink and the mouth piece to your blow drier as well as airplane wings and rockets. In Computational Fluid Dynamics (CFD), the solution to differential equations is approximated using computers and finding new ways to make the methods for obtaining these approximations more efficient is a constant work in progress. In this thesis I am comparing methods for solving these differential equations already used in industry today, to methods that for reasons presented in the thesis might be as good or even better. This is done by using them to approximate the solution to two flow problems representing very different types of flows, the flow around a wind turbine and the flow from to nozzles on a flanged shaft. (Less)
Please use this url to cite or link to this publication:
author
Lindén, Ylva LU
supervisor
organization
course
FMN820 20141
year
type
H2 - Master's Degree (Two Years)
subject
publication/series
Master's Theses in Mathematical Sciences
report number
LUTFNA-3033-2015
ISSN
1404-6342
other publication id
2015:E4
language
English
id
7859277
date added to LUP
2015-11-11 16:27:48
date last changed
2015-12-14 13:32:15
@misc{7859277,
  abstract     = {In modeling unsteady compressible viscous flow problems with the compressible Navier-Stokes equations, time adaptive implicit methods are needed to solve the initial value problems that arise when discretizing the equations in accordance with the method of lines. The methods most used in industrial code today are a family of multistep methods called BDF-methods. Because BDF-methods with higher order than two are not A-stable, and thus do not fulfill necessary stability requirements for CFD-purposes, it is relevant to investigate possible alternatives. SDIRK and ESDIRK-methods are families of implicit Runge-Kutta methods, for which no bound on the order for A-stable schemes have been proven. This thesis uses two different flow problems for comparing a second order BDF-method implemented in SUNDIALS, to SDIRK and ESDIRK methods implemented in TEMPO, a code developed by the University of Kassel.},
  author       = {Lindén, Ylva},
  issn         = {1404-6342},
  language     = {eng},
  note         = {Student Paper},
  series       = {Master's Theses in Mathematical Sciences},
  title        = {Time Adaptive Implicit Methods for Solving Initial Value Problems in CFD},
  year         = {2015},
}