• An exponential time-differencing method for monotonic relaxation systems 

      Aursand, Peder; Evje, Steinar; Flåtten, Tore; Teigen, Knut Erik; Munkejord, Svend Tollak (Journal article; Peer reviewed, 2014)
      We present first and second-order accurate exponential time differencing methods for a special class of stiff ODEs, denoted as monotonic relaxation ODEs. Some desirable accuracy and robustness properties of our methods are ...
    • Hyperbolic Conservation Laws with Relaxation Terms: A Theoretical and Numerical Study 

      Aursand, Peder Kristian (Master thesis, 2011)
      Hyperbolic relaxation systems is an active field of research, with a largenumber of applications in physical modeling. Examples include modelsfor traffic flow, kinetic theory and fluid mechanics. This master s thesis is ...
    • Large Time Step Explicit Schemes for Partial Differential Evolution Equations 

      Solberg, Anders Aase (Master thesis, 2016)
      We consider the large time step (LTS) method for hyperbolic conservation laws, originally proposed by LeVeque in a series of papers over thirty years ago. In particular we have designed a local multi-point LTS scheme, ...
    • Large Time Step Methods for Hyperbolic Partial Differential Equations 

      Nygaard, Rolf (Master thesis, 2017)
      In this thesis we consider explicit finite volume methods that are not limited by the Courant-Friedrichs-Lewy (CFL) condition, referred to as large time step (LTS) methods. LeVequeproposed the first LTS method in the 1980 ...
    • Large Time Step Roe scheme for a common 1D two-fluid model 

      Prebeg, Marin; Flåtten, Tore; Müller, Bernhard (Journal article; Peer reviewed, 2017)
      We present the Large Time Step (LTS) extension of the Roe scheme and apply it to a standard two-fluid model. Herein, LTS denotes a class of explicit methods that are not limited by the CFL (Courant–Friedrichs–Lewy) condition, ...
    • On interface transfer terms in two-fluid models 

      Flåtten, Tore; Morin, Alexandre (Journal article; Peer reviewed, 2012)
      In this note we consider two-fluid models based on the usual formulations for conservation of mass, total momentum and total energy. We present some potentially useful general relationships between the interface exchange ...
    • On solutions to equilibrium problems for systems of stiffened gases 

      Flåtten, Tore; Morin, Alexandre; Munkejord, Svend Tollak (Journal article; Peer reviewed, 2011)
      We consider an isolated system of N immiscible fluids, each following a stiffened-gas equation of state. We consider the problem of calculating equilibrium states from the conserved fluid-mechanical properties, i.e., the ...
    • Relaxation Systems with Applications to Two-Phase Flow 

      Solem, Susanne (Master thesis, 2014)
      Relaxation systems are widely studied and much used to describe nonequilibrium phenomena, occurring in, for example, two-phase flow. In this thesis we will therefore consider relaxation systems in one space dimension and ...
    • Review of two-phase flow models for control and estimation 

      Aarsnes, Ulf Jakob Flø; Flåtten, Tore; Aamo, Ole Morten (Journal article; Peer reviewed, 2016)
      Most model-based control and estimation techniques put limitations on the structure and complexity of the models to which they are applied. This has motivated the development of simplified models of gas-liquid two-phase ...
    • Wave propagation in multicomponent flow models 

      Flåtten, Tore; Morin, Alexandre; Munkejord, Svend Tollak (Journal article; Peer reviewed, 2010)
      We consider systems of hyperbolic balance laws governing flows of an arbitrary number of components equipped with general equations of state. The components are assumed to be immiscible. We compare two such models: one in ...