RL7: Numerical Analysis

Group Leader: Bosco García Archilla

Description:

The research work of RL7 deals with the numerical analysis of the non-linear PDEs arising in the modeling research lines of the Unit. Our aim is to build stable, accurate and fast solvers supported by a sound mathematical analysis. The main difficulties are the instabilities provoked by the discretization,
as in general the discrete problems lose the stability properties of the continuous ones, due to non-linear effects and discretization itself.
We have worked on: design of high-order numerical methods for hyperbolic systems of PDEs that include nonconservative products and/or source terms with good mathematical properties (shock-capturing, well-balanced, etc.), strongly stable stabilized methods for incompressible flows, reduced order modeling of turbulence and energy-stable numerical schemes for two-phase flow with different mass densities.

Members:

Bosco García-Archilla
Macarena Gómez-Marmol
Francisco Guillen González
Juan Vicente Gutiérrez-Santacreu

Research portfolio:

Reduced Order Approximation of fluid flows
  • Mathematical techniques:
    A. POD (Proper Orthogonal Decomposition)-ROM and Reduced Basis discretizations.
    B. Empirical interpolation techniques.
    C. High-accuracy stable discretization techniques.
    D. Error, stability and accuracy analysis (numerical analysis).
Variational Multi-scale approximation of fluid flow equations
  • Mathematical techniques:
    A. Variational Multi-scale discretizations.
    B. Stabilized discretizations, in particular Local Projection Stabilization.
    C. Error, stability and accuracy analysis (numerical analysis).
Stabilization of convection-dominated problems
  • Mathematical techniques:
    A. Energy methods.
    B. Finite-element methods.
    C. Numerical simulation.
  • Application sectors:
    Fluid mechanics, environmental sciences
Computational methods in Fluid Dynamics
  • Mathematical techniques:
    A. Partial Differential Equations
    B. Navier-Stokes equations and related nonlinear problems
    C. Finite element Methods
    D. Numerical Analysis
  • Application sectors:
    Physics, Engineering
High-order finite volume methods for nonlinear hyperbolic systems
  • Mathematical techniques:
    A. Theory of partial differential equations.
    B. Mathematical modelling through conservation laws.
    C. Stability and consistency analysis related to the physics of the problem.
    D. Numerical approximation using finite volume techniques.
    E. Numerical analysis.
  • Application sectors:
    Geophysics, Environment, Aeronautics, Natural hazards risk prevention, Energy, Materials, Aquaculture.
High-order finite volume methods for nonlinear hyperbolic systems: applications to geophysical flow models
  • Mathematical techniques:
    A. Stability and consistency analysis related to the physics of the problem.
    B. Numerical approximation using finite volume techniques.
    C. Numerical analysis.
    D. Scientific software.
    E. GPU implementation.
  • Application sectors:
    Geophysics, Environment, Natural hazards risk prevention.
Evolution equations with nonlocal terms
  • Mathematical techniques:
    A. Numerical complex analysis.
    B. Quadrature.
    C. Numerical methods for ordinary differential equations.
    D. Galerkin methods for partial differential equations.
    E. Hierarchical matrices.
    F. Singular value decomposition.
    G. Scientific Software.
  • Application sectors:
    Civil Engineering, Chemistry, Quantum Physics, Mathematical Finance, Materials, Electromagnetics.

Related projects:

Related transfer: