An adaptive shock-capturing algorithm for solving unsteady reactive flows

A new double flux model is associated with the recent MUSCL-AUSM⁺-triad approach. This coupling allows to do rapid, accurate and stable numerical computations. 1-D and 2-D inert and reactive flows are presented.     

A flux-coordinate-splitting technique for flows with shocks and contact discontinuities

The two-dimensional gasdynamic equations are solved everywhere in the flow field except in regions surrounding the contact discontinuites. A flux-vector-splitting (FVS) technique is applied to the Euler equations so that the directions of propagation of the signals and hence the shocks in the flow can be correctly captured. The split flux equations are solved using conventional second-order-accurate finite difference methods. In the regions surrounding the contact discontinuities, the gasdynamic equations are split into a set of one-dimensional equations. These are transformed in such a way that the density does not appear explicitly in the spatial derivatives of the resultant equations, which are of the Langrangian form. The equations are then solved using second-order-accurate finite difference schemes and numerical smearing of the contact discontinuities is avoided because the dependent variables are continuous across the discontinuities. Consequently, both shocks and contact discontinuities in a two-dimensional gasdynamic flow are accurately resolved. This flux-coordinate-splitting technique is used to calculate the gasdynamic flow in a shock tube, a converging cylindrical shock and the mixing of two supersonic streams. The results are compared with exact solutions and with those deduced from proven numerical techniques. Good correlations are obtained, especially in the sharp definition of contact discontinuities. Therefore, the proposed coordinate-splitting technique improves the resolution of contact discontinuities without affecting the overall calculations of the flow field. In view of this, the coordinate-splitting technique can also be used with other shock capturing techniques besides FVS to achieve the same results.     

A new shock-capturing technique based on Moving Least Squares for higher-order numerical schemes on unstructured grids

This paper presents a shock detection technique based on Moving Least Squares reproducing kernel approximations. The multiresolution properties of these kinds of approximations allow us to define a wavelet function to act as a smoothness indicator. This MLS sensor is used to detect the shock waves. When the MLS sensor is used in a finite volume framework in combination with slope limiters, it improves the results obtained with the single application of a slope-limiter algorithm. The slope-limiter algorithm is activated only at points where the MLS sensor detects a shock. This procedure results in a decrease of the artificial dissipation introduced by the whole numerical scheme. Thus, this new MLS sensor extends the application of slope limiters to higher-order methods. Moreover, as Moving Least Squares approximations can handle scattered data accurately, the use of the proposed methodology on unstructured grids is straightforward. The results are very promising, and comparable to those of essentially non-oscillatory (ENO) and weighted ENO (WENO) schemes. Another advantage of the proposed methodology is its multidimensional character, that results in a very accurate detection of the shock position in multidimensional flows.     

An immersed boundary technique for simulating complex flows with rigid boundary

A new immersed boundary (IB) technique for the simulation of flow interacting with solid boundary is presented. The present formulation employs a mixture of Eulerian and Lagrangian variables, where the solid boundary is represented by discrete Lagrangian markers embedding in and exerting forces to the Eulerian fluid domain. The interactions between the Lagrangian markers and the fluid variables are linked by a simple discretized delta function. The numerical integration is based on a second-order fractional step method under the staggered grid spatial framework. Based on the direct momentum forcing on the Eulerian grids, a new force formulation on the Lagrangian marker is proposed, which ensures the satisfaction of the no-slip boundary condition on the immersed boundary in the intermediate time step. This forcing procedure involves solving a banded linear system of equations whose unknowns consist of the boundary forces on the Lagrangian markers; thus, the order of the unknowns is one-dimensional lower than the fluid variables. Numerical experiments show that the stability limit is not altered by the proposed force formulation, though the second-order accuracy of the adopted numerical scheme is degraded to 1.5 order. Four different test problems are simulated using the present technique (rotating ring flow, lid-driven cavity and flows over a stationary cylinder and an in-line oscillating cylinder), and the results are compared with previous experimental and numerical results. The numerical evidences show the accuracy and the capability of the proposed method for solving complex geometry flow problems both with stationary and moving boundaries.     

Mesoscale simulations of particulate flows with parallel distributed Lagrange multiplier technique

Fluid particulate flows are common phenomena in nature and industry. Modeling of such flows at micro and macro levels as well establishing relationships between these approaches are needed to understand properties of the particulate matter. We propose a computational technique based on the direct numerical simulation of the particulate flows. The numerical method is based on the distributed Lagrange multiplier technique following the ideas of Glowinski et al. [16] and Patankar [30]. Each particle is explicitly resolved on an Eulerian grid as a separate domain, using solid volume fractions. The fluid equations are solved through the entire computational domain, however, Lagrange multiplier constrains are applied inside the particle domain such that the fluid within any volume associated with a solid particle moves as an incompressible rigid body. Mutual forces for the fluid-particle interactions are internal to the system. Particles interact with the fluid via fluid dynamic equations, resulting in implicit fluid-rigid body coupling relations that produce realistic fluid flow around the particles (i.e., no-slip boundary conditions). The particle-particle interactions are implemented using explicit force-displacement interactions for frictional inelastic particles similar to the DEM method of Cundall et al. [10] with some modifications using a volume of an overlapping region as an input to the contact forces. The method is flexible enough to handle arbitrary particle shapes and size distributions. A parallel implementation of the method is based on the SAMRAI (Structured Adaptive Mesh Refinement Application Infrastructure) library, which allows handling of large amounts of rigid particles and enables local grid refinement. Accuracy and convergence of the presented method has been tested against known solutions for a falling particle as well as by examining fluid flows through stationary particle beds (periodic and cubic packing). To evaluate code performance and validate particle contact physics algorithm, we performed simulations of a representative experiment conducted at the U.C. Berkeley Thermal Hydraulic Lab for pebble flow through a narrow opening.     

A generalized-capacity-matrix technique for computing aerodynamic flows

A numerical generalized-capacity-matrix technique is developed for application to aerodynamic flow computations. This technique allows the very fast direct (noniterative) numerical elliptic solvers to be used in poblems with arbitrary internal boundaries and with a wide class of boundary conditions, including numerical application of the Kutta condition on an airfoil without iteration.Accuracy, speed, and usefulness of the technique are demonstrated with linear problems for potential flows over airfoil shapes. The method's main advantages, however, can be exploited within iterative procedures for a variety of complex flow problems governed by systems of equations not necessarily elliptic or linear     

The SPH technique applied to free surface flows

This paper deals with an application of the SPH (Smooth Particle Hydrodynamics) technique to treat free surface problems. The SPH technique was originally conceived and developed for treating astrophysical problems and belongs to the class of “meshless” methods that dispense with the requirement of a computational grid. Instead, a cloud of particles is used to represent the continuum, the contact interaction between them is introduced with their subsequent trajectory being computed in the Lagrangian sense. The design and implementation of the method for transport equations and the Euler inviscid equations is fairly well-documented. Applications to the treatment of free surface flows is however more recent. In this work, the computation of three-dimensional free surface flows with the method is presented. The introduction of Riemann solvers to model the breakup of the initial surface discontinuities between particles is a novel feature of this work. For purposes of illustration, a three-dimensional simulation of the Vaiont dam disaster that occurred in 1963 in northern Italy is presented. This is a case where complicated three-dimensional geometries are involved and was chosen to show-off the versatility of the technique. The results are in general agreement with the qualitative observations and reconstruction of the event as reported by experts. The SPH technique is found to be very promising and powerful for application to free surface flows. In particular, the stage is being reached where for hydraulic problems; it may be used as a powerful simulation tool to delineate high-risk zones downstream of a possible dam failure where geometries of almost arbitrary complexity are involved. At the present time, significant progress is being achieved in developing the technique for application in different domains.     

Sufficient stability conditions in the calculations of steady supersonic flows using the marching technique and time-dependent flows with account for viscosity

The sufficient conditions for the stability and monotonicity in calculating supersonic steady flows by means of the marching technique are derived. The sufficient stability conditions are also obtained for constructing the solutions of time-dependent conservation laws with account for viscosity by explicit difference schemes. With increase in the viscosity coefficient, the conditions derived go over continuously from the hyperbolic to the parabolic constraints on the time step.     

Cyclicity and well-balanced growth in systems with imperfect competition in labor markets

A dynamic macromodel of an economic system with bilateral monopolistic competition in the labor market is considered. Conditions of arising post-classical business cycles in this model are investigated under the assumption that the impact of labor remuneration on the amount of aggregated demand is restricted. Numerical experiments with the model with varied labor productivity demonstrated the possibility of main-line effects. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 29–47, September–October 2007.     

High-order finite-difference implementation of the immersed-boundary technique for incompressible flows

A high-resolution, two-dimensional (2-D), vortex particle method is implemented, and simulations of flows around various bluff bodies are presented, with a detailed analysis of the flow around rectangular cylinders. Long-time simulations of flows around square and rectangular cylinders at low to moderate Reynolds numbers are then performed, and the resulting Strouhal–Reynolds number relationships are compared with experimental and numerical data in the literature. The well-known stepwise variation of the chord-based Strouhal number with chord-to-thickness ratio for rectangular cylinders is replicated, and the flow field is explored and compared with experimental observations. Further analyses with identified vortices provide new insights into the shedding process that leads to the stepwise variation of chord-based Strouhal numbers and the frequency jumps.     

Modelling of navigation based LNA parameters using neural network technique

An approach to model the parameters of LNA which is ideal for GLONASS navigation system. To design LNA, multilayer perceptron architecture is used. The parameters of LNA are calculated using Levenberg Marquardt Backpropagation Algorithm for the frequency range 300 MHz to 18 GHz. ANN model is trained using Agilent MGA 71543 Low Noise Amplifier datasheet and this model shows high regression. The smith and polar charts are plotted for frequency range 300 MHz to 18 GHz and parameters are calculated for center frequency of L1 band of GLONASS, which is 1.602 GHz.     

Modelling with stakeholders

Stakeholder engagement, collaboration, or participation, shared learning or fact-finding, have become buzz words and hardly any environmental assessment or modelling effort today can be presented without some kind of reference to stakeholders and their involvement in the process. This is clearly a positive development, but in far too many cases stakeholders have merely been paid lip service and their engagement has consequentially been quite nominal. Nevertheless, it is generally agreed that better decisions are implemented with less conflict and more success when they are driven by stakeholders, that is by those who will be bearing their consequences. Participatory modelling, with its various types and clones, has emerged as a powerful tool that can (a) enhance the stakeholders knowledge and understanding of a system and its dynamics under various conditions, as in collaborative learning, and (b) identify and clarify the impacts of solutions to a given problem, usually related to supporting decision making, policy, regulation or management. In this overview paper we first look at the different types of stakeholder modelling, and compare participatory modelling to other frameworks that involve stakeholder participation. Based on that and on the experience of the projects reported in this issue and elsewhere, we draw some lessons and generalisations. We conclude with an outline of some future directions.     

Micro and macro scale technique for strongly coupled two-phase flows simulation

The calculation results for a direct-flow chemical vapor deposition (CVD) reactor model are presented. Chemical condensation is considered at a small volume fraction of the dispersed phase. Phase formation stages are simulated numerically for various values of the Damköehler number over a large time interval. The calculations made it possible to identify the structures of solid-phase nucleus growth on the channel wall and in the two-phase mixture flow.     

A well-balanced flux-vector splitting scheme designed for hyperbolic systems of conservation laws with source terms

We propose a way to construct robust numerical schemes for the computations of numerical solutions of one- and two-dimensional hyperbolic systems of balance laws. In order to reduce the computational cost, we selected the family of flux vector splitting schemes. We reformulate the source terms as nonconservative products and treat them directly in the definition of the numerical fluxes by means of generalized jump relations. This is applied to a 1D shallow water system with topography and to a 2D simplified model of two-phase flows with damping effects. Numerical results and comparisons with a classical centered discretizations scheme are supplied.     

Circulant preconditioning technique for barrier options pricing under fractional diffusion models

In recent years, considerable literature has proposed the more general class of exponential Lévy processes as the underlying model for prices of financial quantities, which thus better explain many important empirical facts of financial markets. Finite moment log stable, Carr–Geman–Madan–Yor and KoBoL models are chosen from those above-mentioned models as the dynamics of underlying equity prices in this paper. With such models pricing barrier options, one kind of financial derivatives is transformed to solve specific fractional partial differential equations (FPDEs). This study focuses on numerically solving these FPDEs via the fully implicit scheme, with the shifted Grünwald approximation. The circulant preconditioned generalized minimal residual method which converges very fast with theoretical proof is incorporated for solving resultant linear systems. Numerical examples are given to demonstrate the effectiveness of the proposed preconditioner and show the accuracy of our method compared with that done by the Fourier cosine expansion method as a benchmark.     

Realistic rendering with turbulent flows

This paper focuses on realistic rendering of scenes which include turbulent flows. In this respect we suggest solving the Navier–Stokes equations through a simple approach which offers better steadiness than classical methods. Then we adapt a ray‐tracing algorithm to treat convection motions by deflecting ray paths: we obtain effects of rendering through heat. Copyright © 2000 John Wiley & Sons, Ltd.     

Modelling and simulation of the multi-scroll chaotic attractors using bond graph technique

This paper presents modelling and simulation of multi-scroll chaotic attractors by using a new simple and more general bond graph model. For this purpose, the multi-segment non-linear resistor in Chua’s circuit is modelled by using piecewise linearization with control inequalities. The proposed model consists of active/passive circuit elements, voltage-controlled current source (VCCS) and ideal switches. The advantage of modelling multi-segment non-linear resistor by using control inequalities yields minimum number of the switches and sources. Proposed model is simple and more general and, especially, could be used in various kinds of non-linear circuit in the chaos studies. Generally, two different non-linear resistor models are used in the literature to obtain odd and even numbers of the scrolls. In this study, one model is developed for both multi-scroll chaotic attractors. In this paper, bond graph simulation of Chua’s circuit is realized by using proposed model. The BONDAS program that developed in Matlab is used for the simulations, and satisfactory results are obtained.