Impact of Stefan blowing and magnetic dipole on bio-convective flow of Maxwell nanofluid over a stretching sheet

The features of ferromagnetic fluids make it supportive for an extensive usage in loudspeakers, magnetic resonance imaging, computer hard drives, directing of magnetic drug and magnetic hyperthermia. Owing to all such potential applications, the current investigation is to understand the relationship between the thermal distribution, magnetic field and resulting fluid flow of Maxwell liquid over a stretching sheet. Investigation of thermal energy and concentration is carried out in the presence of thermal radiation, non-uniform heat sink/source, chemical reaction, Stefan blowing, magnetic dipole, thermophoresis and Brownian motion. Also, microorganisms are considered just to stabilize the suspended nanoparticles. Boundary layer approximation is employed during mathematical derivation. Based on a new constitutive relation, the governing equations are formulated and are reduced into a coupled non-linear system of equations using appropriate transformations. Further, these equations are solved numerically using fourth-order Runge–Kutta method with shooting technique. The impact of involved parameters is discussed and analysed graphically. Outcomes disclose that Newtonian liquid shows high heat transfer when compared to non-Newtonian (Maxwell) liquid for increased values of Brownian motion and thermophoresis parameters. Increased values of Peclet number declines the rate of gyrotactic microorganisms. Finally, an increase in Brownian and thermophoresis motion parameters declines the rate of heat transfer.

Parallel Implementation of the SHYFEM Model

This paper presents the MPI-based parallelization of the three-dimensional hydrodynamic model SHYFEM (System of HydrodYnamic Finite Element Modules). The original sequential version of the code was parallelized in order to reduce the execution time of high-resolution configurations using state-of-the-art HPC systems. A distributed memory approach was used, based on the message passing interface (MPI). Optimized numerical libraries were used to partition the unstructured grid (with a focus on load balancing) and to solve the sparse linear system of equations in parallel in the case of semi-to-fully implicit time stepping. The parallel implementation of the model was validated by comparing the outputs with those obtained from the sequential version. The performance assessment demonstrates a good level of scalability with a realistic configuration used as benchmark.

The ISOTILT software for discovering cooperative rigid-unit rotations in networks of interconnected rigid units

A user-friendly web-based software tool called `ISOTILT' is introduced for detecting cooperative rigid-unit modes (RUMs) in networks of interconnected rigid units (e.g. molecules, clusters or polyhedral units). This tool implements a recently described algorithm in which symmetry-mode patterns of pivot-atom rotation and displacement vectors are used to construct a linear system of equations whose null space consists entirely of RUMs. The symmetry modes are first separated into independent symmetry-mode blocks and the set of equations for each block is solved separately by singular value decomposition. ISOTILT is the newest member of the ISOTROPY Software Suite. Here, it is shown how to prepare structural and symmetry-mode information for use in ISOTILT, how to use each of ISOTILT's input fields and options, and how to use and interpret ISOTILT output.

Semi-Elimination Methodology for Simulating High Flow Features in a Reservoir

Despite the rapid rise of computing power and advances in computational techniques in past decades, it is still challenging in reservoir simulation to model complex and detailed features that are represented by small cells with large permeability values, for example, fractures, multi-segment wells, etc. While those features may carry a large amount of flow and thus have a significant impact on the performance prediction, the combination of small volume and large permeability unfortunately leads to well-known time stepping and convergence difficulties during Newton iteration. We address this issue of high flow through small cells by developing a new semi-elimination computational technique. At the beginning of simulation, we construct a set of pressure basis which is a mapping from pressures at surrounding cells in the bulk of reservoir to pressures at those small cells. Next, we start the time-stepping scheme. For each time step or iteration within a time step, small cells are first employed to provide an accurate computation of flow rates and derivatives using upstream weighting and a flow partitioning scheme. Afterwards, small cells are eliminated and a linear system of equations is assembled and solved involving only bulk cells. This semi-elimination technique allows us to fundamentally avoid the drawbacks caused by including small cells in the global system of equations, while capturing their effect on the flow of hydrocarbon in the reservoir. One of the advantages of the proposed techniques over other existing methods is that it is fully implicit and preserves upstream weighting and compositions of the flow field even after small cells are eliminated, which enhances numerical stability and accuracy of simulation results. Application of this technique to several synthetic and field models demonstrates significant performance and accuracy improvement over standard approaches. This method thus offers a practical way to model complex and dynamic flow behaviors in important features without incurring penalties in speed and robustness of the simulation.

Distributed GPU Based Matrix Power Kernel for Geoscience Applications

High-performance computing is at the heart of digital technology which allows to simulate complex physical phenomena. The current trend for hardware architectures is toward heterogeneous systems with multi-core CPUs accelerated by GPUs to get high computing power. The demand for fast solution of Geoscience simulations coupled with new computing architectures drives the need for challenging parallel algorithms. Such applications based on partial differential equations, requires to solve large and sparse linear system of equations. This work makes a step further in Matrix Powers Kernel (MPK) which is a crucial kernel in solving sparse linear systems using communication-avoiding methods. This class of methods deals with the degradation of performances observed beyond several nodes by decreasing the gap between the time necessary to perform the computations and the time needed to communicate the results. The proposed work consists of a new formulation for distributed MPK kernels for the cluster of GPUs where the pipeline communications could be overlapped by the computation. Also, appropriate data reorganization decreases the memory traffic between processors and accelerators and improves performance. The proposed structure is based on the separation of local and external components with different layers of interface nodes-due to the MPK algorithm-. The data is restructured in a way where all the data required by the neighbor process comes contiguously at the end, after the local one. Thanks to an assembly step, the contents of the messages for each neighbor are determined. Such data structure has a major impact on the efficiency of the solution, since it permits to design an appropriate communication scheme where the computation with local data can occur on the GPUs and the external ones on the CPUs. Moreover, it permits more efficient inter-process communication by an effective overlap of the communication by the computation in the asynchronous pipeline way. We validate our design through the test cases with different block matrices obtained from different reservoir simulations : fractured reservoir dual-medium, black-oil two phase-flow, and three phase-flow models. The experimental results demonstrate the performance of the proposed approach compared to state of the art. The proposed MPK running on several nodes of the GPU cluster provides a significant performance gain over equivalent Sparse Matrix Vector product (SpMV) which is already optimized and provides better scalability.

Optimal design of optical analog solvers of linear systems

In this paper, given a linear system of equations $$\mathbf {A}\, \mathbf {x}= \mathbf {b}$$ A x = b , we are finding locations in the plane to place objects such that sending waves from the source points and gathering them at the receiving points solves that linear system of equations. The ultimate goal is to have a fast physical method for solving linear systems. The issue discussed in this paper is to apply a fast and accurate algorithm to find the optimal locations of the scattering objects. We tackle this issue by using asymptotic expansions for the solution of the underlying partial differential equation. This also yields a potentially faster algorithm than the classical BEM for finding solutions to the Helmholtz equation.

Covariances in Pólya urn schemes

By now there is a solid theory for Polya urns. Finding the covariances is somewhat laborious. While these papers are “structural,” our purpose here is “computational.” We propose a practicable method for building the asymptotic covariance matrix in tenable balanced urn schemes, whereupon the asymptotic covariance matrix is obtained by solving a linear system of equations. We demonstrate the use of the method in growing tenable balanced irreducible schemes with a small index and in critical urns. In the critical case, the solution to the linear system of equations is explicit in terms of an eigenvector of the scheme.

On Linear and Non-Linear Approximation In the Theory of Convective Heat Transfer

A system of linear equations that is currently widely used to describe convective heat transfer does not seem to be able to explain some experimental facts. One of the reasons for this may lie in using Newton’s and Fourier’s linear laws when deriving energy and Navier-Stokes equations. Replacing linear equations with nonlinear ones, as well as using an expression for surface heat flux density that is based on laws of physics instead of expressions called ‘cooling laws,’ would allow to solve a wider range of problems, and also would better agree with the experimental data. The use of proposed non-linear system of equations would also permit engineers in chemical, textile, defense, power, and other industries to design more economical and smaller-sized heat exchange devices.

Refinement of Multiparameters Overrelaxation (RMPOR) Method

In this paper, we present refinement of multiparameters overrelaxation (RMPOR) method which is used to solve the linear system of equations. We investigate its convergence properties for different matrices such as strictly diagonally dominant matrix, symmetric positive definite matrix, and M-matrix. The proposed method minimizes the number of iterations as compared with the multiparameter overrelaxation method. Its spectral radius is also minimum. To show the efficiency of the proposed method, we prove some theorems and take some numerical examples.

A Strategy for Fine Mesh Resolution in Contact Mechanics

To obtain detail in elastic, frictional contact problems involving contact many — at least tens, and more suitably hundreds [1] — of nodes are necessary over the contact patch. Generally, this fine discretization results in intractable numbers of system equations that must be solved, but this problem is greatly mitigated when the elasticity of the contacting bodies is represented by elastic compliance matrices rather than stiffness matrices. An examination of the classical analytic expressions for the contact of disks — an example of smooth contact — shows that for most standard engineering metals, such as brass, steel, or titanium, the pressures that would cause more than one degree of arc of contact would push the materials past the elastic limit. The discretization necessary to capture the interface tractions would be on the order of at least tens of nodes. With the resulting boundary integral formulation would involve several hundreds of nodes over the disk, and the corresponding finite element mesh would have tens of thousands. The resulting linear system of equations must be solved at each load step and the numerical problem becomes extremely difficult or intractable. A compliance method of facilitating extremely fine contact patch resolution can be achieved by exploiting Fourier analysis and the Michell solution. The advantages of this compliance method are that only degrees of freedom on the surface are introduced and those not in the region of contact are eliminated from the system of equations to be solved.