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
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
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
A. Energy methods.
B. Finite-element methods.
C. Numerical simulation.
Fluid mechanics, environmental sciences
Computational methods in Fluid Dynamics
A. Partial Differential Equations
B. Navier-Stokes equations and related nonlinear problems
C. Finite element Methods
D. Numerical Analysis
Physics, Engineering
High-order finite volume methods for nonlinear hyperbolic systems
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.
Geophysics, Environment, Aeronautics, Natural hazards risk prevention, Energy, Materials, Aquaculture.
High-order finite volume methods for nonlinear hyperbolic systems: applications to geophysical flow models
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.
Geophysics, Environment, Natural hazards risk prevention.
Evolution equations with nonlocal terms
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.
Civil Engineering, Chemistry, Quantum Physics, Mathematical Finance, Materials, Electromagnetics.
Related projects:
- Modelling and computation of shocks and interfaces
- Modelos multicapa no-hidrostáticos relajados y métodos numéricos de alto orden bien equilibrados para flujos geofísicos
- Accurate numerical methods for free-surface flows
- Desarrollo de simuladores hidrodinámicos y morfodinámicos eficientes para la evaluación y previsión de riesgos II
- Desarrollo, análisis e implementación eficiente de métodos numéricos de alto orden para modelos simplificados de fluidos con incertidumbre en los datos
- Relaxed non-hydrostatic multilayer models and high-order well-balanced numerical MEthods for GeophysicAl FLOWs
- Development of efficient hydrodynamic and morphodynamic simulators for risk assessment and forecasting
- Well balanced high order numerical methods for nonlinear hyperbolic systems. Applications to the simulation of geophysical flows
- Well Balanced High Order Numerical Methods for Nonlinear Hyperbolic Systems: Application to Design of Mathematical Tools for Early Warning of Natural Disasters
- Accurate Roms for Insdustrial Applications
- Modelización de Orden Reducido Orientada al Diseño Eco-Eficiente de Edificios
- ROM Optimization for Architecture and Design
- Modelización de Orden Reducido de componentes de sub-malla en Métodos de Multiescala Variacional
- Nuevas técnicas numéricas para ecuaciones en derivadas parciales disipativas
- Adaptive numerical techniques for the long term dynamics of dissipative partial differential equations
- PDEs for Biological models with Chemotaxis and Nonlocal effects
- High Order Positive schemes for the Keller-Segel Problem
Related transfer:
- Design of a theoretical framework to derive high-order numerical methods for hyperbolic systems of PDEs that include nonconservative products and/or source terms with good mathematical properties
- Accurate analysis of courtyard thermal performance with application to project design in Architecture
- Faster than real time tsunami modeling
- Use of innovative HPC techniques for faster than real time simulations
- Integration of Tsunami-HySEA as the mathematical model of the Spanish and Italian Tsunami Early Warning Systems
- Integration of Tsunami-HySEA in existing general purpose Natural Hazards tools
