A high-order Cartesian-grid finite-volume method for aeroacoustics simulations

The simulated annealing algorithm is used to seek optimal radiant heater configurations that provide a desired distribution of incident radiant energy onto a surface. The problem is motivated by a need to create well-understood boundary conditions that simulate fire environments. A bank of halogen lamps irradiates the back of a thin black plate (called a shroud), which simulates the fire environment. For such fire simulations, shroud temperatures routinely exceed 1000 °C and thermal radiation is the dominant mode of heat transfer. The test specimen is then heated by placing it in front of the shroud. The panel, accommodating the radiant heaters (lamps), provides equally spaced slots all of which are powered at the same voltage. Lamp positioning is crucial to obtaining a uniform temperature on the shroud, but determining the best positioning of the lamps experimentally through trial and error has proven difficult. The discrete optimization problem searches possible lamp configurations by simulating adding or removing lamps from the panel. Inverse heat transfer methods have been successfully applied to similar problems. Applying inverse heat transfer methods to this problem, the desired boundary conditions on the shroud are used to solve for the required heater settings. Two boundary conditions are needed: the temperature profile and the heat flux profile on the shroud. The heat flux profile is determined by calculating the radiation heat transfer between the shroud and the test object. However, because the heaters used in the design can only assume discrete positions and are all maintained at the same power level, traditional inverse methods fail. A discrete inverse radiation heat transfer solution method is needed. In this study, a simulated annealing optimization routine is used to determine optimal heater positions given desired boundary conditions on the shroud. Computational characteristics of simulated annealing are presented as well as results of the optimization.

There are now many successful applications of 2D finite difference flood simulations on rectangular grids. However, finite volume algorithms are now starting to take over as the preferred choice for simulating flood inundation. The use of finite volume algorithms allows the simulation to be based on irregular meshes. Yet many users are not convinced of the benefits of irregular meshing. This is partly because meshing adds a rather unwelcome extra process to the modelling. But it is more likely because the process of generating irregular meshes has been problematic and time consuming. In the rush to develop excellent finite volume flow engines, meshing has been rather left behind. Yet the quality of the flow modelling depends on the quality of the meshing. The authors have been working on innovative mesh generation techniques. The aim has been to come up with a faster, more reliable mesh generation process. But also to improve the resulting mesh in order to speed up the hydraulic simulation and to generate better quality flood inundation results. This paper discusses and illustrates these advances in meshing. Results are presented to show how well the meshing techniques deal with problematic boundaries. The resulting meshes are applied to test cases to show the impact of either grids or different qualities of mesh on flood inundation results for a variety of circumstances.

The least square-based finite difference-finite volume (LSFD-FV) method has been developed and successfully applied to solve various two-dimensional flow problems with a high-order of accuracy. In this paper, the extension of the LSFD-FV method to the three-dimensional (3D) case on unstructured grids is presented. Different from other existing high-order methods, the LSFD-FV method combines the good features of the least square-based finite difference (LSFD) scheme for derivative approximation and the finite volume (FV) discretization for conservation of physical laws. Within each control cell, a high-order polynomial resultant from a Taylor series expansion is used to approximate the solution in the FV discretization of governing equations, where the derivatives are approximated by the LSFD scheme. As a result, the mesh-free nature of the LSFD scheme endows the LSFD-FV method with the flexibility on unstructured grids. Additionally, the straightforward algorithm of the LSFD scheme and the direct utilization of the Taylor series polynomial make the LSFD-FV method user-friendly and easy to implement. Furthermore, the inviscid and viscous fluxes are simultaneously evaluated by lattice Boltzmann and gas kinetic flux solvers in this work, which avoids additional and complicated treatment for the viscous discretization. Accuracy studies on unstructured hexahedral and tetrahedral grids validate the third-order of accuracy of the 3D LSFD-FV method. Various 3D incompressible and compressible numerical experiments are also presented. The results show that the proposed method enjoys the higher accuracy than the conventional second-order method on the same mesh. When the same accuracy is achieved, the present high-order method has superior computational efficiency to the second-order counterpart.

Shock waves interacting with multi-material interfaces in compressible flows result in complex shock diffraction patterns involving total or partial reflection, refraction and transmission of the impinging shock wave. To simulate such complicated interfacial dynamics problems, a fixed Cartesian grid approach in conjunction with level set interface tracking is attractive. In this regard, a unified Riemann solver based Ghost Fluid Method (GFM) was developed to accurately resolve and represent the embedded solid and fluid object(s) in high speed compressible multiphase flows. While the GFM-based Cartesian grid approach significantly alleviates the complexity associated with mesh management, the method lacks flexibility in effective grid point placement in regions with rich structures in the flow field. Thus for higher-order and highly accurate sharp interface Cartesian grid based calculations with optimal computational effort, it is imperative to supplement the solution with adaptive mesh refinement technique. Hence in this work, a simple procedure is presented to complement the Riemann solver based GFM approach with quadtree (octree in three dimensions) based Local Mesh Refinement (LMR) technique for efficient and high fidelity computations involving strong shock interactions in multiphase compressible flows. The paper reports on a simple, conservative formulation for accurate calculation of ENO-based numerical fluxes at the fine-coarse mesh boundary. The numerical examples displayed in this paper clearly demonstrate that the methodology is consistent in generating satisfactory solutions, and effectively capturing fine structures in the flow.

In this paper, we consider a new spectral finite volume method (FVM) for the elastic wave equations. Our new FVM is based on a piecewise constant approximation on a fine mesh and a high-order polynomial reconstruction on a coarser mesh. Our new method is constructed based on two existing techniques, the high-order FVM and the spectral FVM. In fact, we will construct a new method to take advantage of both methods. More precisely, our method has two distinctive features. The first one is that the local polynomial reconstructions are performed on the coarse triangles and the reconstruction matrices for all the coarse triangles are the same. This fact enhances the parallelization of our algorithm. We will present a parallel implementation of our method and show excellent efficiency results. The second one is that, by using a suitable number of finer triangles with a coarse triangle, we obtain an overdetermined reconstruction system, which can enhance the robustness of the reconstruction process. To derive our scheme, standard finite volume technique is applied to each fine triangle, and the high-order reconstructed polynomials, computed on coarse triangles, are used to compute numerical fluxes. We will present numerical results to show the performance of our method. Our method is presented for 2-D problems, but the same methodology can be applied to 3-D.

This paper presents a compact high-order finite volume method based on recording the weighted integral value of a function on a grid cell. Extending the general finite volume method, it employs a single unit template and a limiter method to suppress oscillations, addressing the convection-diffusion equation. By utilizing implicit methods for nonlinear and linear solvers of the discrete equation, the scheme achieves enhanced compactness, accuracy, and computational efficiency.

The use of the finite-volume method for predicting radiation heat transfer in a participating medium has gained some popularity because it fits well with modern finite-volume methods of computation fluid dynamics. This article consists of three parts: the rationale underlying the finite-volume method is discussed, a comparison of the finite-volume and discrete ordinates methods is presented, and results obtained by application of the method to several problems (two of which might serve as benchmark problems) are reported.

Recently, the Cartesian grid method was used on simulations of fluid flow around the complex geometry problems. In this paper, the Cartesian grid method with cut cells are used to simulate incompressible viscous flows around moving objects. In this study, the small cut cells are merged with neighboring cells. The code was developed based on Fractional Step Method on Finite Volume Method. In time integrate, the second order explicit Adams-Bashforth method was used for the convective terms and second order implicit Crank-Nicholson method was used for the diffusive terms. Some moving boundary problem are simulated using the presented code and compared with other previous numerical and experimental results.

A novel subdomain adaptive integral method (SAIM) is presented for fast analysis of electromagnetic radiation and scattering from three dimensional objects of arbitrary shape. In conventional AIM, a uniform Cartesian grid is built up to entirely enclose the object, and auxiliary point sources are used to efficiently calculate far-zone interactions. However, adopting one Cartesian grid will actually cause large amount of auxiliary point sources redundant for the far-zone interaction calculation. To reduce the excess of those redundant auxiliary point sources, in the proposed SAIM, the whole domain is divided into several subdomains and then each subdomain is properly enclosed in its smaller Cartesian grid. Furthermore, the current continuity boundary condition between adjacent subdomains is employed to ensure the accuracy. Compared with the conventional AIM, the proposed SAIM technique can significantly reduce the number of auxiliary point sources and improve the convergence of iterative process. Numerical examples show the accuracy and efficiency of the proposed technique.

Development of a dynamic artificial neural network model of an absorption chiller and its experimental validation

An experimental investigation, supported by analysis, was performed to determine the heat transfer characteristics for turbulent flow in a circular tube with circumferentially varying wall temperature and wall heat flux. Air was the working fluid. The desired boundary conditions were achieved by electric heating within the wall of a tube whose thickness varied circumferentially. In this way, ratios of maximum-to-minimum wall heat flux as large as two were attained. Local heat transfer coefficients, deduced from the experimental data, display a circumferential variation that is substantially smaller than the heat flux variation. In general, lower heat transfer coefficients correspond to circumferential locations of greater heating, while higher coefficients correspond to locations of lesser heating. The predictions of prior analyses appear to overestimate the circumferential variation of the heat transfer coefficient. A specially designed probe was employed to measure the radial and circumferential temperature distributions within the flowing airstream. On the basis of these measurements, as well as from the heat transfer results, it is concluded that, in the neighborhood of the wall, the tangential turbulent diffusivity is greater than the radial turbulent diffusivity. The axial thermal development was found to be more rapid on the lesser-heated side of the tube than on the greater-heated side. Experimentally determined circumferential-average heat transfer coefficients agreed well with the predictions of analysis.

An effective numerical technique for solving a special class of ordinary difference equations

ABSTRACTIn this article, an efficient analytical method for elastically restrained Euler columns embedded in an elastic medium has been proposed to calculate buckling loads. The lateral deflection function under compression is represented by a Fourier sine series. Stokes’ transformation is employed to develop the legitimized stability equations. Explicit analytical expressions are derived, which can be used for any type of boundary conditions. The efficiency of present formulation is demonstrated by comparing the results to those obtained by imposing three well-known boundary conditions available in the literature. A very good agreement has been obtained. The present formulation permits to have more efficient coefficient matrix for calculating the buckling loads of Euler columns with any desired boundary conditions.

A new numerical method to determine isothermal g-functions of borehole heat exchanger fields

In this paper, our main goal is to present a non-classical MPFA method coupled with a high order finite volume method for the simulation of oil water displacements in heterogeneous and anisotropic petroleum reservoirs using general polygonal meshes. The governing equations are solved using the IMPES (IMplicit Pressure and Explicit Saturation) strategy, where the elliptic pressure equation is discretized by a linear Multipoint Flux Approximation method using Harmonic points (MPFA-H) capable to handle strongly heterogeneous and anisotropic media. Besides, to approximate the advective term that characterizes the hyperbolic saturation equation, we use the Multidimensional Optimal Order Detection (MOOD) method. This technique is based in an “a posteriori” limitation procedure, i.e., the limitation procedure is done after the calculation of “candidate solutions” only where necessary to guarantee certain physical properties such as monotonicity. To show the potential of our finite volume formulation, we solve some benchmark problems found in literature.