Cascade Lattice Research Articles

Generalized interpolation-supplemented cascaded lattice Boltzmann method for noise radiated from a circular cylinder

Flow past a stationary or vibrating body usually leads to intense noise radiation. In order to study this problem via direct simulations, a cascaded lattice Boltzmann method (CLBM) is developed in the moving frame of reference, and implemented in a body-fitted grid using the generalized interpolation-supplemented particle streaming. A far-field perfectly matched layer is also incorporated so as to avoid sound reflection. The proposed generalized interpolation-supplemented cascaded lattice Boltzmann method (GICLBM) is then validated through numerical experiments concerning fixed and forced oscillating circular cylinders, in terms of forces exerting on the cylinder, wall stress, near-field flow dynamics, and far-field sound radiation. Very good consistency is observed for all quantities discussed therein with previous benchmark tests. Furthermore, the noise radiated from a circular cylinder undergoing vortex-induced vibration (VIV) is investigated using the GICLBM, providing interesting results. Firstly, at a mass ratio of m⁎=2, the flow and vibration dynamics are found to be dependent on the Mach number, and the critical value is found to be approximately Ma=0.1. Secondly, through comparisons with scenarios involving a fixed cylinder and a forced vibrating cylinder, it is noted that the VIV generates significantly more complicated sound sources including monopole and drag dipole. Thirdly, in the lock-in condition, the increase in the reduced velocity only alters the magnitude of the radiated sound pressure but not the directivity. Through this study, a high-fidelity, efficient, and relatively simple framework for fluid-structure-sound interactions is proposed.

Direct simulations of external flow and noise radiation using the generalized interpolation-supplemented cascaded lattice Boltzmann method

Direct simulations of external flow and the associated noise radiation are studied by an improved lattice Boltzmann method, i.e., the generalized interpolation-supplemented cascaded lattice Boltzmann method (GICLBM). In this method, the cascaded collision scheme is used to improve the numerical stability of the conventional collision schemes, and the generalized interpolation approach is used in the particle streaming process so as to allow a non-uniform and body-fitted mesh partition. With that, both near- and far-field flow dynamics and noise radiation are resolved simultaneously. In order to capture sound waves, the perfectly matched layer is also implemented so as to avoid waves reflecting to and polluting the inner acoustic field. Moreover, a novel index technique is developed for the GICLBM to enable implicit streaming, which brings an efficient memory reduction. Three cases are then performed to showcase the feasibility, accuracy, extensibility, and efficiency of the present framework, including flow past a square cylinder, flow past an elliptic cylinder, and flow past a NACA 0012 airfoil, each implemented with a type of body-fitted mesh. Both the fluid dynamic and noise radiation are found to be in good agreement with results using the Navier–Stokes solvers. This study demonstrates the potential of the GICLBM for accurately and efficiently simulating external problems as well as sound generation and propagation.

Cascaded lattice Boltzmann method for thermal flows on standard lattices

In this paper, a thermal cascaded lattice Boltzmann method (TCLBM) is developed in combination with the double-distribution-function (DDF) approach on the standard D2Q9 lattice. A density distribution function relaxed by the cascaded scheme based on central moments is employed to solve the flow field, and a total energy distribution function relaxed by the BGK scheme is used to solve the temperature field. The two distribution functions are coupled naturally to provide a new TCLBM. In this method, the viscous heat dissipation and compression work are taken into account, the Prandtl number and specific-heat ratio are adjustable, and the external force is considered directly without the Boussinesq assumption. The TCLBM is validated by numerical experiments of the thermal Couette flow, low-Mach number shock tube problem, Rayleigh-Bénard convection, and natural convection in a square cavity with a large temperature difference. The simulation results agree well with the analytical solutions and/or results given by previous researchers.

PROTEUS: A coupled iterative force-correction immersed-boundary cascaded lattice Boltzmann solver for moving and deformable boundary applications

Many realistic fluid flow problems are characterised by high Reynolds numbers and complex moving or deformable geometries. In our previous study, we presented a novel coupling between an iterative force-correction immersed boundary and a multi-domain cascaded lattice Boltzmann method, Falagkaris et al., and investigated flows around rigid bodies at Reynolds numbers up to 105. Here, we extend its application to flows around moving and deformable bodies with prescribed motions. Emphasis is given on the influence of the internal mass on the computation of the aerodynamic forces including deforming boundary applications where the rigid body approximation is no longer valid. Both the rigid body and the internal Lagrangian points approximations are examined. The resulting solver has been applied to viscous flows around an in-line oscillating cylinder, a pitching foil, a plunging SD7003 airfoil and a plunging and flapping NACA-0014 airfoil. Good agreement with experimental results and other numerical schemes has been obtained. It is shown that the internal Lagrangian points approximation accurately captures the internal mass effects in linear and angular motions, as well as in deforming motions, at Reynolds numbers up to 4⋅104. In all cases, the aerodynamic loads are significantly affected by the internal fluid forces.

PROTEUS: A coupled iterative force-correction immersed-boundary multi-domain cascaded lattice Boltzmann solver

Most realistic fluid flow problems are characterized by high Reynolds numbers and complex boundaries. Over the last ten years, immersed boundary methods that are able to cope with realistic geometries have been applied to Lattice-Boltzmann (LB) methods. These methods, however, have normally been applied to low Reynolds number problems. Here we present a novel coupling between an iterative force-correction immersed boundary (Zhang et al., 2016) and a multi-domain cascaded LB method. The iterative force-correction immersed boundary method has been selected due to the improved accuracy of the computation, while the cascaded LB formulation is used due to its superior stability at high Reynolds numbers. The coupling is shown to improve both the stability and numerical accuracy of the solution. The resulting solver has been applied to viscous flow (up to a Reynolds number of 100000) passed a NACA-0012 airfoil at a 10 degree angle of attack. Good agreement with results obtained using a body-fitted Navier–Stokes solver has been obtained. The formulation provides a straight forward and efficient method for modeling realistic geometries and could easily be extended to problems with moving boundaries.

Cascade Lattice Micromechanics Model for the Effective Permeability of Materials with Microcracks

AbstractWithin the framework of mean-field homogenization methods, a lattice version of the cascade micromechanics model for the estimation of the effective permeability of microcracked materials w...

Adaptive lattice IIR filtering revisited: convergence issues and new algorithms with improved stability properties

Several algorithms for adaptive IIR filters parameterized in lattice form can be found in the literature. The salient feature of these structures when compared with the direct form is that ensuring stability is extremely easy. On the other hand, while computing the gradient signals that drive the direct form update algorithms is straightforward, it is not so for the lattice algorithms. This has led to simplified lattice algorithms using gradient approximations. Although, in general, these simplified schemes present the same stationary points as the original algorithms, whether this is also true for convergent points has remained an open problem. This also applies to nongradient-based lattice algorithms such as hyperstability based and the Steiglitz-McBride algorithms. Here, we answer this question in the negative, by showing that for several adaptive lattice algorithms, there exist settings in which the stationary point corresponding to identification of the unknown system is not convergent. In addition, new lattice algorithms with properties are derived. They are based on the cascade lattice structure, which allows the derivation of sufficient conditions for local stability.

Cascade lattice IIR adaptive filters

The feedback lattice filter forms, including the two-multiplier form and the normalized form, are examined with respect to their relationships to the feedback direct form filter. Specifically, the transformation matrix between the lattice forms and the direct form is derived; parameter and state relationships between the lattice forms and the direct form are therefore obtained. An IIR filter structure-the cascade lattice IIR structure-is constructed. Based on this structure, three IIR adaptive filtering algorithms in the two-multiplier form can then be developed following the gradient approach, the Steiglitz-McBride approach and the hyperstability approach. Convergence of these algorithms is theoretically analyzed using either the ODE approach or the hyperstability theorem. These algorithms are then simplified into forms computationally as efficient as their corresponding direct form algorithms. Relationships of the simplified algorithms to the direct form algorithms are also studied, which disclose a consistency in algorithm structure regardless of the filter form. Three normalized lattice algorithms can also be derived from the two-multiplier lattice algorithms. Experimental results show much improved performance of the normalized lattice algorithms over the two-multiplier lattice algorithms and the direct form algorithms.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Comments, with reply, on "A new efficient adaptive cascade lattice structure" by M. Tummala and S.R. Parker

In the above-titled paper (see ibid., vol.CAS-34, p.707-711, July 1987) the authors present a least-mean-square (LMS)-based Approach for adapting a canonical cascade lattice structure, in order to perform general-purpose adaptive finite impulse response (FIR) filtering tasks. The commenters discuss the tradeoffs involved in choosing between this approach and competing techniques. The authors essentially agree with the comments.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Synthesis of recursive digital filters by state feedback of non‐recursive cascaded lattice filters

AbstractA general method to realize any digital transfer function is presented. The method is understood as a two‐stage process. First, a non‐recursive system having the same transfer zeros as the given transfer function is synthesized in the form of a special cascaded lattice structure. Then the poles of the non‐recursive system, which occur exclusively at the origin, are shifted by extending this system through state feedback so that the shifted poles coincide with the poles of the specified transfer function while the transfer zeros remain unchanged.1 Compared with the well‐known cascaded lattice structures proposed by Mitra et al.2 the resulting filters exhibit advantages in the realization of the adders. Furthermore, it is pointed out how the cascaded lattice structure2 can be derived from the structure introduced here by applying a state transformation.

Realization of digital transfer functions using cascaded lattice and ladder block structures

Several techniques are available for implementing a scalar digital filter using lattice and ladder structures which are known to yield low noise realizations. Of these, the lattice and ladder structures proposed by Gray and Markel have the advantage of being internally scaled. Block implementation of a scalar digital filter offers a number of advantages. In this paper, new algorithms to realize block digital filters in the form of cascaded lattice or ladder two-pairs are proposed. Block lattice and ladder structures similar to Gray and Markel's scalar structure are obtained by using Levinson recursion. Also, normalized block lattice and ladder structures are developed.