Viscous flow computations using a meshless solver, LSFD-U

The Upwind-Least Squares Finite Difference (LSFD-U) scheme has been successfully applied for inviscid flow computations. In the present work, we extend the procedure for computing viscous flows. Different ways of discretizing the viscous fluxes are analysed for the positivity, which determines the robustness of the solution procedure. The scheme which is found to be more positive is employed for viscous flux computation. The numerical results for validating the procedure are presented.

Analytical and simulation studies of a multiprocessor system for high-speed numerical computations

This paper describes the architecture of a multiprocessor system which we call the Broadcast Cube System (BCS) for solving important computation intensive problems such as systems of linear algebraic equations and Partial Differential Equations (PDEs), and highlights its features. Further, this paper presents an analytical performance study of the BCS, and it describes the main details of the design and implementation of the simulator for the BCS.

Turbulent flow computations on a hybrid cartesian point distribution using meshless solver LSFD-U

This paper may be considered as a sequel to one of our earlier works pertaining to the development of an upwind algorithm for meshless solvers. While the earlier work dealt with the development of an inviscid solution procedure, the present work focuses on its extension to viscous flows. A robust viscous discretization strategy is chosen based on positivity of a discrete Laplacian. This work projects meshless solver as a viable cartesian grid methodology. The point distribution required for the meshless solver is obtained from a hybrid cartesian gridding strategy. Particularly considering the importance of an hybrid cartesian mesh for RANS computations, the difficulties encountered in a conventional least squares based discretization strategy are highlighted. In this context, importance of discretization strategies which exploit the local structure in the grid is presented, along with a suitable point sorting strategy. Of particular interest is the proposed discretization strategies (both inviscid and viscous) within the structured grid block; a rotated update for the inviscid part and a Green-Gauss procedure based positive update for the viscous part. Both these procedures conveniently avoid the ill-conditioning associated with a conventional least squares procedure in the critical region of structured grid block. The robustness and accuracy of such a strategy is demonstrated on a number of standard test cases including a case of a multi-element airfoil. The computational efficiency of the proposed meshless solver is also demonstrated. (C) 2010 Elsevier Ltd. All rights reserved.

Modelling and analysis of the variance in parallelism in parallel computations

In this paper, we introduce an analytical technique based on queueing networks and Petri nets for making a performance analysis of dataflow computations when executed on the Manchester machine. This technique is also applicable for the analysis of parallel computations on multiprocessors. We characterize the parallelism in dataflow computations through a four-parameter characterization, namely, the minimum parallelism, the maximum parallelism, the average parallelism and the variance in parallelism. We observe through detailed investigation of our analytical models that the average parallelism is a good characterization of the dataflow computations only as long as the variance in parallelism is small. However, significant difference in performance measures will result when the variance in parallelism is comparable to or higher than the average parallelism.

Automatic decomposition of unstructured meshes employing genetic algorithms for parallel FEM computations

Parallel execution of computational mechanics codes requires efficient mesh-partitioning techniques. These mesh-partitioning techniques divide the mesh into specified number of submeshes of approximately the same size and at the same time, minimise the interface nodes of the submeshes. This paper describes a new mesh partitioning technique, employing Genetic Algorithms. The proposed algorithm operates on the deduced graph (dual or nodal graph) of the given finite element mesh rather than directly on the mesh itself. The algorithm works by first constructing a coarse graph approximation using an automatic graph coarsening method. The coarse graph is partitioned and the results are interpolated onto the original graph to initialise an optimisation of the graph partition problem. In practice, hierarchy of (usually more than two) graphs are used to obtain the final graph partition. The proposed partitioning algorithm is applied to graphs derived from unstructured finite element meshes describing practical engineering problems and also several example graphs related to finite element meshes given in the literature. The test results indicate that the proposed GA based graph partitioning algorithm generates high quality partitions and are superior to spectral and multilevel graph partitioning algorithms.

Turbulent flow computations using upwind RANS technique for a flat plate and an airfoil

Reynolds Averaged Navier Stokes (RANS) equations are solved using third order upwind biased Roe's scheme for the inviscid fluxes and second order central difference scheme for the viscous fluxes. The Baldwin & Lomax turbulence model is employed for Reynolds stresses. The governing equations are solved using finite-volume implicit scheme in body fitted curvilinear coordinate O-grid system. Computations axe reported for a flat plate apart from RAE 2822 and NACA 0012 airfoils. Results for the flat plate at M = 0.3, R-c = 4.0 x 10(6) compare favourably with the analytical solution. Results for the two airfoils are compared with experiment. There is a good agreement in C-p distribution between experiment and computation for both the airfoils. Comparison of C-f distribution with experiment for RAE 2822 airfoil is reasonable.

Matrix Processors Using p-adic Arithmetic for Exact Linear Computations

A unique code (called Hensel's code) is derived for a rational number by truncating its infinite p-adic expansion. The four basic arithmetic algorithms for these codes are described and their application to rational matrix computations is demonstrated by solving a system of linear equations exactly, using the Gaussian elimination procedure.

Error, Confidence, and Cost in Engineering Computations

The questions that one should answer in engineering computations - deterministic, probabilistic/randomized, as well as heuristic - are (i) how good the computed results/outputs are and (ii) how much the cost in terms of amount of computation and the amount of storage utilized in getting the outputs is. The absolutely errorfree quantities as well as the completely errorless computations done in a natural process can never be captured by any means that we have at our disposal. While the computations including the input real quantities in nature/natural processes are exact, all the computations that we do using a digital computer or are carried out in an embedded form are never exact. The input data for such computations are also never exact because any measuring instrument has inherent error of a fixed order associated with it and this error, as a matter of hypothesis and not as a matter of assumption, is not less than 0.005 per cent. Here by error we imply relative error bounds. The fact that exact error is never known under any circumstances and any context implies that the term error is nothing but error-bounds. Further, in engineering computations, it is the relative error or, equivalently, the relative error-bounds (and not the absolute error) which is supremely important in providing us the information regarding the quality of the results/outputs. Another important fact is that inconsistency and/or near-consistency in nature, i.e., in problems created from nature is completely nonexistent while in our modelling of the natural problems we may introduce inconsistency or near-inconsistency due to human error or due to inherent non-removable error associated with any measuring device or due to assumptions introduced to make the problem solvable or more easily solvable in practice. Thus if we discover any inconsistency or possibly any near-inconsistency in a mathematical model, it is certainly due to any or all of the three foregoing factors. We do, however, go ahead to solve such inconsistent/near-consistent problems and do get results that could be useful in real-world situations. The talk considers several deterministic, probabilistic, and heuristic algorithms in numerical optimisation, other numerical and statistical computations, and in PAC (probably approximately correct) learning models. It highlights the quality of the results/outputs through specifying relative error-bounds along with the associated confidence level, and the cost, viz., amount of computations and that of storage through complexity. It points out the limitation in error-free computations (wherever possible, i.e., where the number of arithmetic operations is finite and is known a priori) as well as in the usage of interval arithmetic. Further, the interdependence among the error, the confidence, and the cost is discussed.

An embedded grid adaptation strategy for unstructured data based finite volume computations

A grid adaptation strategy for unstructured data based codes, employing a combination of hexahedral and prismatic elements, generalizable to tetrahedral and pyramidal elements has been developed.

Integrated parallelization of computations and visualization for large-scale applications

Critical applications like cyclone tracking and earthquake modeling require simultaneous high-performance simulations and online visualization for timely analysis. Faster simulations and simultaneous visualization enable scientists provide real-time guidance to decision makers. In this work, we have developed an integrated user-driven and automated steering framework that simultaneously performs numerical simulations and efficient online remote visualization of critical weather applications in resource-constrained environments. It considers application dynamics like the criticality of the application and resource dynamics like the storage space, network bandwidth and available number of processors to adapt various application and resource parameters like simulation resolution, simulation rate and the frequency of visualization. We formulate the problem of finding an optimal set of simulation parameters as a linear programming problem. This leads to 30% higher simulation rate and 25-50% lesser storage consumption than a naive greedy approach. The framework also provides the user control over various application parameters like region of interest and simulation resolution. We have also devised an adaptive algorithm to reduce the lag between the simulation and visualization times. Using experiments with different network bandwidths, we find that our adaptive algorithm is able to reduce lag as well as visualize the most representative frames.

Premixed flame response to equivalence ratio fluctuations: Comparison between reduced order modeling and detailed computations

Combustion instability events in lean premixed combustion systems can cause spatio-temporal variations in unburnt mixture fuel/air ratio. This provides a driving mechanism for heat-release oscillations when they interact with the flame. Several Reduced Order Modelling (ROM) approaches to predict the characteristics of these oscillations have been developed in the past. The present paper compares results for flame describing function characteristics determined from a ROM approach based on the level-set method, with corresponding results from detailed, fully compressible reacting flow computations for the same two dimensional slot flame configuration. The comparison between these results is seen to be sensitive to small geometric differences in the shape of the nominally steady flame used in the two computations. When the results are corrected to account for these differences, describing function magnitudes are well predicted for frequencies lesser than and greater than a lower and upper cutoff respectively due to amplification of flame surface wrinkling by the convective Darrieus-Landau (DL) instability. However, good agreement in describing function phase predictions is seen as the ROM captures the transit time of wrinkles through the flame correctly. Also, good agreement is seen for both magnitude and phase of the flame response, for large forcing amplitudes, at frequencies where the DL instability has a minimal influence. Thus, the present ROM can predict flame response as long as the DL instability, caused by gas expansion at the flame front, does not significantly alter flame front perturbation amplitudes as they traverse the flame. (C) 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved.