A GPU-based algorithm for efficient LES of high Reynolds number flows in heterogeneous CPU/GPU supercomputers

Αn optimized MPI+OpenACC implementation model that performs efficiently in CPU/GPU systems using large-eddy simulation is presented. The code was validated for the simulation of wave boundary-layer flows against numerical and experimental data in the literature. A direct Fast-Fourier-Transform-based solver was developed for the solution of the Poisson equation for pressure taking advantage of the periodic boundary conditions. This solver was optimized for parallel execution in CPUs and outperforms by 10 times in computational time a typical iterative preconditioned conjugate gradient solver in GPUs. In terms of parallel performance, an overlapping strategy was developed to reduce the overhead of performing MPI communications using GPUs. As a result, the weak scaling of the algorithm was improved up to 30%. Finally, a large-scale simulation (Re = 2 × 10⁵) using a grid of 4 × 10⁸ cells was executed, and the performance of the code was analyzed. The simulation was launched using up to 512 nodes (512 GPUs + 6144 CPU-cores) on one of the current top 10 supercomputers of the world (Piz Daint). A comparison of the overall computational time showed that the GPU version was 4.2 times faster than the CPU one. The parallel efficiency of this strategy (47%) is competitive compared with the state-of-the-art CPU implementations, and it has the potential to take advantage of modern supercomputing capabilities.     

Permutation trinomials over Fq3

We consider four classes of polynomials over the fields ${\mathbb{F}}_{q^3}$, $q=p^h$, $p>3$, $f_1(x)=x^{q^2+q-1}+A{x}^{q^2-q+1}+Bx$, $f_2(x)=x^{q^2+q-1}+A{x}^{q^3-q^2+q}+Bx$, $f_3(x)=x^{q^2+q-1}+A{x}^{q^2}-Bx$, $f_4(x)=x^{q^2+q-1}+A{x}^q-Bx$, where $A,B\in {\mathbb{F}}_q$. We find sufficient conditions on the pairs $(A,B)$ for which these polynomials permute ${\mathbb{F}}_{q^3}$ and we give lower bounds on the number of such pairs.     

Global existence of weak solutions for the 3D chemotaxis-Navier–Stokes equations

In this paper, we consider the Cauchy problem for the three dimensional chemotaxis-Navier–Stokes equations. By exploring the new a priori estimates, we prove the global existence of weak solutions for the 3D chemotaxis-Navier–Stokes equations.     

Strain-dependent internal parameters in hyperelastic biological materials

The behavior of hyperelastic energies depending on an internal parameter, which is a function of the deformation gradient, is discussed. As an example, the analysis of two models where the parameter describes the activation of a tetanized skeletal muscle tissue is presented. In those models, the activation parameter depends on the strain and it is shown the importance of considering the derivative of the parameter with respect to the strain in order to capture the proper stress–strain relations.     

On the skin friction coefficient in viscoelastic wall-bounded flows

Analysis of the skin friction coefficient for wall bounded viscoelastic flows is performed by utilizing available direct numerical simulation (DNS) results for viscoelastic turbulent channel flow. The Oldroyd-B, FENE-P and Giesekus constitutive models are used. First, we analyze the friction coefficient in viscous, viscoelastic and inertial stress contributions, as these arise from suitable momentum balances, for the flow in channels and pipes. Following Fukagata et al. (Phys. Fluids, 14, p. L73, 2002) and Yu et al. (Int. J. Heat. Fluid Flow, 25, p. 961, 2004) these three contributions are evaluated averaging available numerical results, and presented for selected values of flow and rheological parameters. Second, based on DNS results, we develop a universal function for the relative drag reduction as a function of the friction Weissenberg number. This leads to a closed-form approximate expression for the inverse of the square root of the skin friction coefficient for viscoelastic turbulent pipe flow as a function of the friction Reynolds number involving two primary material parameters, and a secondary one which also depends on the flow. The primary parameters are the zero shear-rate elasticity number, El₀, and the limiting value for the drag reduction at high Weissenberg number, LDR, while the secondary one is the relative wall viscosity, μ_w. The predictions reproduce both types A and B of drag reduction, as first introduced by Virk (Nature, 253, p. 109, 1975), corresponding to partially and fully extended polymer molecules, respectively. Comparison of the results for the skin friction coefficient against experimental data shows good agreement for low and moderate drag reduction which is the region covered by the simulations.     

High order closed Newton-Cotes exponentially and trigonometrically fitted formulae as multilayer symplectic integrators and their application to the radial Schr?dinger equation

In this paper we study the connection between: (i) closed Newton-Cotes formulae of high order, (ii) trigonometrically-fitted and exponentially-fitted differential methods, (iii) symplectic integrators. Several one step symplectic integrators have been produced based on symplectic geometry during the last decades (see the relevant literature and the references here). However, the study of multistep symplectic integrators is very poor. In this paper we investigate the High Order Closed Newton-Cotes Formulae and we write them as symplectic multilayer structures. We develop trigonometrically-fitted and exponentially-fitted symplectic methods which are based on the closed Newton-Cotes formulae. We apply the symplectic schemes in order to solve the resonance problem of the radial Schr?dinger equation. Based on the theoretical and numerical results, conclusions on the efficiency of the new obtained methods are given.     

The d-very ampleness of adjoint line bundles on quasi-elliptic surfaces

In this paper, we give a numerical criterion of Reider-type for the d-very ampleness of the adjoint line bundles on quasi-elliptic surfaces, and meanwhile we give a new proof of the vanishing theorem on quasi-elliptic surfaces emailed from Langer and show that it is the optimal version.     

Construction and application of photoresponsive smart nanochannels

In living organisms, many biological processes are inextricably linked with light, such as the photosynthesis systems and rhodopsin. Hence, construction of light-sensitive biomimetic-nanochannels, which can realize the functions of cells and other membrane structures with high degree of spatial and temporal control, is particularly attractive and challenging. As a cornerstone of light-sensitive nanochannels, the photoresponsive materials are a big family and at their mature stage after several decades of development, which can provide different strategies to construct biomimetic photoresponsive nanochannels. In this review, we mainly summarize the construction and applications of photoresponsive nanochannels on the basis of various photoresponsive materials. The construction of photoresponsive nanochannels can be classified into four categories: photoresponsive inorganic nanochannels based on inorganic-compound-based photonic sensitive materials; photoresponsive organic nanochannels based on organic-compound-based photonic sensitive materials; photoresponsive polymers nanochannel based on photoresponsive polymers materials and potential photoresponsive nanochannels based on other photoresponsive materials. After introducing the construction of photoresponsive nanochannels, the review highlights some of the most recent applications of photoresponsive nanochannels in separation, energy conversion and storage, drug delivery and so on.     

A mathematical model for the admission process in intensive care units

A mathematical model is given for the admission process in Intensive Care Units (ICUs). It is shown that the model exhibits bistability for certain values of its parameters. In particular, it is observed that in a two-dimensional parameter space, two saddle-node bifurcation curves terminate at a single point of the cusp bifurcation, creating an enclosed region in which the model has one unstable and two stable states. It is shown that in the presence of bistability, variations in the value of parameters may lead to undesired outcomes in the admission process as the value of state variables abruptly changes. Using numerical simulations, it is also discussed how such outcomes can be avoided by appropriately adjusting the parameter values.