A Fast Hybrid Pressure-Correction Algorithm for Simulating Incompressible Flows by Projection Methods

For simulating incompressible flows by projection methods. it is generally accepted that the pressure-correction stage is the most time-consuming part of the flow solver. The objective of the present work is to develop a fast hybrid pressure-correction algorithm for numerical simulation of incompressible flows around obstacles in the context of projection methods. The key idea is to adopt different numerical methods/discretizations in the sub-steps of projection methods. Here, a classical second-order time-marching projection method which consists of two sub-steps is chosen for the purpose of demonstration. In the first sub-step, the momentum equations are discretized on unstructured grids and solved by conventional numerical methods, here, a meshless method. In the second sub-step (pressure-correction), the proposed algorithm adopts a double discretization system and combines the weighted least squares approximation with the essence of immersed boundary methods. Such a design allows us to develop a FFT-based solver to speed up the solution of the pressure Poisson equation for flow cases with obstacles, while keeping the implementation of boundary conditions for the momentum equations as easy as conventional numerical methods do with unstructured grids. Numerical experiments of five test cases have been performed to verify and validate the proposed hybrid algorithm and evaluate its computational performance. The results show that the new FFT-based hybrid algorithm is working and robust, and it is significantly faster than the multigrid-based reference method. The hybrid algorithm opens an avenue for the development of next-generation high-performance parallel computational fluid dynamics solvers for incompressible flows

New constitutive equations derived from a kinetic model for melts and concentrated solutions of linear polymers

In this paper, new constitutive equations for linear entangled polymer solutions and melts are derived from a recently proposed kinetic model (Fang et al. 2004) by using five closure approximations available in the literature. The simplest closure approximation considered is that due to Peterlin (1966). In this case, a mean-field-type Fokker-Planck equation underlying the evolution equation for an equilibrium averaged polymer segment orientation tensor is shown to be consistent with the fluctuation-dissipation theorem (Kubo et al. 1985). We compare the performance of the five new constitutive equations in their capacity to faithfully reproduce the predictions of the modified encapsulated FENE dumbbell model of Fang et al. (2004) for a number of shear and extensional flows. Comparisons are also made with the experimental data of Kahvand (1995) and Bhattacharjee et al. (2002, 2003). In the case of the Hinch-Leal and Bingham closures (Hinch and Leal 1976; Chaubal and Leal 1998) a combination with the quadratic closure of Doi (1981) is found to be necessary for stability in fast flows. The Hinch-Leal closure approximation, modified in this way, is found to outperform the other closures and its mathematical description is considerably simpler than that of the Bingham closur

A non-homogeneous constitutive model for human blood. Part 1. Model derivation and steady flow

The earlier constitutive model of Fang & Owens (Biorheology, vol. 43, 2006, p. 637) and Owens (J. Non-Newtonian Fluid Mech. vol. 140, 2006, p. 57) is extended in scope to include non-homogeneous flows of healthy human blood. Application is made to steady axisymmetric flow in rigid-walled tubes. The new model features stress-induced cell migration in narrow tubes and accurately predicts the Fåhraeus-Lindqvist effect whereby the apparent viscosity of healthy blood decreases as a function of tube diameter in sufficiently small vessels. That this is due to the development of a slippage layer of cell-depleted fluid near the vessel walls and a decrease in the tube haematocrit is demonstrated from the numerical results. Although clearly influential, the reduction in tube haematocrit observed in small-vessel blood flow (the so-called Fåhraeus effect) does not therefore entirely explain the Fåhraeus-Lindqvist effec

Flow over Hills: A Large-Eddy Simulation of the Bolund Case

Simulation of local atmospheric flows around complex topography is important for several applications in wind energy (short-term wind forecasting and turbine siting and control), local weather prediction in mountainous regions and avalanche risk assessment. However, atmospheric simulation around steep mountain topography remains challenging, and a number of different approaches are used to represent such topography in numerical models. The immersed boundary method (IBM) is particularly well-suited for efficient and numerically stable simulation of flow around steep terrain. It uses a homogenous grid and permits a fast meshing of the topography. Here, we use the IBM in conjunction with a large-eddy simulation (LES) and test it against two unique datasets. In the first comparison, the LES is used to reproduce experimental results from a wind-tunnel study of a smooth three-dimensional hill. In the second comparison, we simulate the wind field around the Bolund Hill, Denmark, and make direct comparisons with field measurements. Both cases show good agreement between the simulation results and the experimental data, with the largest disagreement observed near the surface. The source of error is investigated by performing additional simulations with a variety of spatial resolutions and surface roughness propertie

A MLS-based lattice spring model for simulating elasticity of materials

A MLS-based lattice spring model is presented for numerical modeling of elasticity of materials. In the model, shear springs between particles are introduced in addition to normal springs. However, the unknowns contain only particle displacements but no particle rotations. The novelty of the model lies in that the deformations of shear springs are computed by using the local strain obtained by the moving least squares (MLS) approximation rather than using the particle displacements directly. By doing so, the proposed lattice spring model can represent the diversity of Poisson's ratio without violating the requirement of rotational invariance. Relationships between micro spring parameters and macro material constants are derived from the Cauchy-born rules and the hyperelastic theory. Numerical examples show that the proposed model is able to reproduce elastic solutions obtained by finite element methods for problems without fractures. Therefore, it is capable of simulating solid materials which are initially continuous, but eventually fracture when critical stress and/or displacement levels are reached. A demonstrating example is presented

Explainable Modeling for Wind Power Forecasting: A Glass-Box Approach with Exceptional Accuracy

Machine learning models (e.g., neural networks) achieve high accuracy in wind power forecasting, but they are usually regarded as black boxes that lack interpretability. To address this issue, the paper proposes a glass-box approach that combines exceptional accuracy with transparency for wind power forecasting. Specifically, advanced artificial intelligence methods (e.g., gradient boosting) are innovatively employed to create shape functions within the forecasting model. These functions effectively map the intricate non-linear relationships between wind power output and input features. Furthermore, the forecasting model is enriched by incorporating interaction terms that adeptly capture interdependencies and synergies among the input features. Simulation results show that the proposed glass-box approach effectively interprets the results of wind power forecasting from both global and instance perspectives. Besides, it outperforms most benchmark models and exhibits comparable performance to the best-performing neural networks. This dual strength of transparency and high accuracy positions the proposed glass-box approach as a compelling choice for reliable wind power forecasting.Comment: It was submitted to the 23rd Power Systems Computation Conference (PSCC 2024) in September 202

Towards oscillation-free implementation of the immersed boundary method with spectral-like methods

It is known that, when the immersed boundary method (IBM) is implemented within spectral-like methods, the Gibbs oscillation seriously deteriorates the calculation of derivatives near the body surface. In this paper, a radial basis function (RBF) based smoothing technique is proposed with the intention of eliminating or efficiently reducing the Gibbs oscillation without affecting the flow field outside the body. Based on this technique, a combined IBM/spectral scheme is developed to solve the incompressible Navier-Stokes equations. Numerical simulations of flow through a periodic lattice of cylinders of various cross sections are performed. The results demonstrate that the proposed methodology is able to give accurate and nearly oscillation-free numerical solutions of incompressible viscous flows. (C) 2011 Elsevier Inc. All rights reserved

A coupled distinct lattice spring model for rock failure under dynamic loads

It is necessary to take into account the micro discretization of natural rock when studying its macroscopic failure behavior. This requirement has resulted in renewed and increased interest in the discrete or framework/lattice numerical modeling techniques. However, to fully construct a numerical model for practical applications using a discrete numerical model is computationally difficult with current computing technologies. Hence, a coupled model has been developed to overcome this limitation by coupling the Distinct Lattice Spring Model (DLSM) and the Numerical Manifold Method (NMM). In the coupled model, the microscopic discrete model of the rock is represented by a system of discrete particles interacting via springs while the macroscopic level model is represented by the NMM. The proposed model bears a structure of three layers corresponding to the DLSM model, the NMM model, and a model for coupling, respectively. The coupling model is based on a newly developed Particle based Manifold Method (PMM) to bridge the DLSM with the NMM. The proposed coupled model can reduce the computational resources needed for the purely discrete particle based model. This study introduces theoretical aspects of the coupled model together with a few examples to demonstrate its correctness and feasibility. (C) 2011 Elsevier Ltd. All rights reserved