Seminario Daniel Domínguez Vázquez (IDAEA-CSIC)
Speaker: Daniel Domínguez Vázquez, Spanish National Research Council (IDAEA-CSIC)
Title: "A hyperbolic description of mixing".
Date and time: 17 December, 11:00
Venue: Salón de Grados B, EII.
Abstract: A description of mixing based on a Liouville master equation is introduced. The Liouville approach allows to treat the problem of solute transport deterministically in Lagrangian form combining characteristics of the classical formulations based on the Fokker-Planck (FP) and Langevin equations. The hyperbolicity of the Liouville master equation allows to trace the concentrations along characteristic lines in the augmented phase space composed by solute particle locations and a set of random coefficients used to define the noise term added to the system (see Fig. 1), in lieu of time-dependent stochastic processes [1,2]. This circumvents the use of stochastic calculus and eliminates the diffusive term of the master equation, at the expense of increasing the dimensionality of the joint probability density function (PDF) of solute particle locations. The Liouville approach is unaffected by the Courant-Friedrichs-Lewy (CFL) stability condition, does not suffer from Gibbs oscillations, does not require (order-reducing) filtering and regularization techniques, and it does not rely on sampling. Because of these reasons it offers more accuracy and a lower computational cost in comparison to Eulerian grid-based and Lagrangian particle tracking solvers. In this talk, I will discuss these methodological advantages and show how the Liouville approach can be used to analytically describe the evolution of arbitrarily shaped blobs of solute in an ambient steady incompressible flow in a coordinate system that moves and rotates along streamlines.
Speaker: Daniel Domínguez Vázquez, Spanish National Research Council (IDAEA-CSIC)
Title: "A hyperbolic description of mixing".
Date and time: 17 December, 11:00
Venue: Salón de Grados B, EII.
Abstract: A description of mixing based on a Liouville master equation is introduced. The Liouville approach allows to treat the problem of solute transport deterministically in Lagrangian form combining characteristics of the classical formulations based on the Fokker-Planck (FP) and Langevin equations. The hyperbolicity of the Liouville master equation allows to trace the concentrations along characteristic lines in the augmented phase space composed by solute particle locations and a set of random coefficients used to define the noise term added to the system (see Fig. 1), in lieu of time-dependent stochastic processes [1,2]. This circumvents the use of stochastic calculus and eliminates the diffusive term of the master equation, at the expense of increasing the dimensionality of the joint probability density function (PDF) of solute particle locations. The Liouville approach is unaffected by the Courant-Friedrichs-Lewy (CFL) stability condition, does not suffer from Gibbs oscillations, does not require (order-reducing) filtering and regularization techniques, and it does not rely on sampling. Because of these reasons it offers more accuracy and a lower computational cost in comparison to Eulerian grid-based and Lagrangian particle tracking solvers. In this talk, I will discuss these methodological advantages and show how the Liouville approach can be used to analytically describe the evolution of arbitrarily shaped blobs of solute in an ambient steady incompressible flow in a coordinate system that moves and rotates along streamlines.
