Numath

Tools

Optimization, Stability and Sensitivity

On the stability analysis of compressible and turbulent Navier-Stokes flows, a smart and efficient use of computational and human resources is an asset. NUMATH team has integrated a number of public libraries (PETSc, SLEPc, MUMPS, among others) into zTAUev, an in-house code that permits the calculation of the associated large scale eigenvalue problem. Based on a discrete formulation (first-discretize-then-linearize), it allows to extract the so-called …

numath_tools

Optimization Algorithms and Game Theory

Optimization Algorithms and Game Theory An optimization tool is developed specially for stability problems, which consists of optimization algorithms, geometry parametrization and mesh deformation, a dynamically updated surrogate model, design of experiments and a mode tracking scheme. The real part of an eigenvalue represents the growth/decay rate of the corresponding eigenmode. When the real part of this eigenvalue is positive, the eigenmode is unstable and …

numath_reserch_bg

Lattice Boltzmann Method

Research Our research line in the lattice Boltzmann methods (LBM) focuses the analysis of the collision operator. The collision operator is of critical importance in the LBM method, as it is responsible of the proper modelization of the physics. The Lattice Boltzmann method (LBM) is becoming one of the most interesting alternative because it is able to overcome some of the traditional CFD limitations. However, …

Numath-DMD

Dinamic Mode Decomposition (DMD)

Dynamic Mode Decomposition (DMD) is a feature detection algorithm that allows to identify recurring patterns from a temporally resolved data sequence. The technique is compatible with both data either generated from numerical computations and or obtained from experimental measurements. The two major advantages of DMD-based analysis are: I. It enforces a data-driven paradigm, which makes innecessary the knowledge of an underlying mathematical model.II. It provides …

Horses3D

Overview HORSES3D is a 3D parallel code that uses the high–order Discontinuous Galerkin Spectral Element Method (DGSEM) and is written in modern object–oriented Fortran (2008+). The code is currently being developed at ETSIAE–UPM (the School of Aeronautics of the Universidad Politécnica de Madrid). HORSES3D is built on the NSLITE3D code by David A. Kopriva, which is based on the book “Implementing Spectral Methods for Partial …