Francisco Mandujano

Mesoscopic constitutive relations for dilute polymer solutions

A novel approach to the dynamics of dilute solutions of polymer molecules under flow conditions is proposed by applying the rules of mesoscopic nonequilibrium thermodynamics (MNET). The probability density describing the state of the system is taken to be a function of the position and velocity of the molecules, and on a local vector parameter accounting for its deformation. This function obeys a generalized Fokker–Planck equation, obtained by calculating the entropy production of the system, and identifying the corresponding probability currents in terms of generalized forces. In simple form, this coarse-grained description allows one to derive hydrodynamic equations where molecular deformation and diffusion effects are coupled. A class of non-linear constitutive relations for the pressure tensor are obtained. Particular models are considered and compared with experiments.

Moments Preserving and high-resolution Semi-Lagrangian Advection Scheme

We present a forward semi-Lagrangian numerical method for systems of transport equations able to advect smooth and discontinuous fields with high-order accuracy. The numerical scheme is composed of an integration of the transport equations along the trajectory of material elements in a moving grid and a reconstruction of the fields in a reference regular mesh using a non-linear mapping and adaptive moment-preserving interpolations. The non-linear mapping allows for the arbitrary deformation of material elements. Additionally, interpolations can represent discontinuous fields using adaptive-order interpolation near jumps detected with a slope-limiter function. Due to the large number of operations during the interpolations, a serial implementation of this scheme is computationally expensive. The scheme has been accelerated in many-core parallel architectures using a thread per grid node and parallel data gathers. We present a series of tests that prove the scheme to be an attractive option for simulating advection equations in multi-dimensions with high accuracy.

A Template for Scalable Continuum Dynamic Simulations in Multiple GPUs

In this work we present a programming philosophy and a template code for achieving computational scalability when using multiple graphics processing units (GPUs) in the numerical solution of any mathematical system of equations found in continuum dynamic simulations. The programming philosophy exploits the principal characteristics of the GPU hardware, with emphasis in the delivering of threads with massive memory fetches, intense calculations using local registers and limited writes to global memory. The philosophy requires explicit formulas for calculations for which domain decomposition is trivial. The domains are decomposed in regions that use the local central processing unit (CPU) to communicate common interfaces using the message passing interface (MPI). A template code for the heat equation is established and tested for scalability. The novelty is that we show a series of codes, constructed from the basic template, that solve all the basic model equations found in continuum dynamics, and present illustrative results. The model equations are the heat equation, the Poisson equation, the shallow-water equations, the flow in porous media equations and the vorticity equations.

On the forced flow around a rigid flapping foil

The two dimensional incompressible viscous flow past a flapping rigid foil immersed in a uniform stream is studied using a lattice-Boltzmann model. When the foil’s center of mass is fixed in space, numerical results reproduce the transition from the von Karman (vKm) to the inverted von Karman wake [T. Schnipper, A. Andersen, and T. Bohr, “Vortex wakes of a flapping foil,” J. Fluid Mech. 633, 411 (2009) and A. Das, R. K. Shukla, and R. N. Govardhan, “Existence of a sharp transition in the peak propulsive efficiency of a low pitching foil,” J. Fluid Mech. 800, 307 (2016)]. Beyond the inverted vKm transition, the foil was released. The numerical results show that the hydrodynamic forces on the flapper are oscillatory functions of time with amplitudes and mean values that scale with the square of the Strouhal number, defined with either the flapping amplitude or the flapper length that decays an order of magnitude when the foil is freed to swim. Upstream swimming consisted of a uniform horizontal motion and a vertical heaving. The swimming speed showed a linear dependence on the Strouhal number, defined with the amplitude of oscillation of the foil tip. As a consequence, thrust generated by the free flapper is related to the square of the swimming speed for moderate Reynolds numbers.The two dimensional incompressible viscous flow past a flapping rigid foil immersed in a uniform stream is studied using a lattice-Boltzmann model. When the foil’s center of mass is fixed in space, numerical results reproduce the transition from the von Karman (vKm) to the inverted von Karman wake [T. Schnipper, A. Andersen, and T. Bohr, “Vortex wakes of a flapping foil,” J. Fluid Mech. 633, 411 (2009) and A. Das, R. K. Shukla, and R. N. Govardhan, “Existence of a sharp transition in the peak propulsive efficiency of a low pitching foil,” J. Fluid Mech. 800, 307 (2016)]. Beyond the inverted vKm transition, the foil was released. The numerical results show that the hydrodynamic forces on the flapper are oscillatory functions of time with amplitudes and mean values that scale with the square of the Strouhal number, defined with either the flapping amplitude or the flapper length that decays an order of magnitude when the foil is freed to swim. Upstream swimming consisted of a uniform horizontal motion and a...

CFD on Graphic Cards

In the last decade, the entertainment and graphic design industries demand for higher resolution and more realistic graphics has motivated graphic card manufacturers to develop high performance graphic processing units (GPUs) at low cost. Nowadays GPUs are highly efficient parallel processing units that can be used for general purposes. Such developments open a new alternative within scientific computation, promising high performance parallel computation at everyones reach. Graphic cards seem to be an attractive option, specially for research groups and institutions with limited computational resources and for teaching purposes. Here, an overview of parallel computation on GPUs is presented, as well as the efforts to manipulate and promote this technology within the UNAM, particularly in Fluid Mechanics applications.