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Application and numerical error analysis of multiscale method for air flow, heat and pollutant transfer through different scale urban areas

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BUILDING AND ENVIRONMENT 2019年 149卷 349-365页

作者： Cui, Peng-Yi Zhang, Yan Zhang, Jin-Hao Huang, Yuan-Dong Tao, Wen-Quan Univ Shanghai Sci & Technol Sch Environm & Architecture Shanghai Peoples R China Xi An Jiao Tong Univ Sch Energy & Power Engn Key Lab Thermofluid Sci & Engn MOE Xian Shaanxi Peoples R China

There is an increasing concern on the effect of the outdoor environment on the indoor air quality (IAQ) through ventilation. In urban areas, the physical phenomenon that the air pollutants pass over the neighborhood scale-street scale-indoor scale, and affect the health of the residents belongs to multiscale problems. The adopted multiscale method models the problem in nesting grid system approach by solving from top (entire domain with relative coarse grids) to down (subsequent sub-domains with finer grid). In this paper, a 3-D multiscale model with Richardson number (Ri) equal to 0.85 was firstly established to investigate the above multiscale phenomenon, then evaluated by comparing with the full-scale intensive simulation, since our previous study showed that when Ri <= 0.85 the standard k-epsilon turbulence model can better predict the flow and temperature fields. The numerical error analysis of the multiscale method was conducted by considering the effects of two aspects (boundary condition interpolation schemes and sub-domain partitioning) on the regularity of error production and transfer. Results show that the applied multiscale method can save 83.8% computing time. Furthermore, it can be concluded that among the three interpolation schemes for the boundary reconstruction the linear and spline interpolation methods are appropriate while the nearest method should not be applied because of its 1st-order accuracy. If insensitive interfaces are chosen as the partitioning interfaces of the lower-scale domain the computational accuracy of the multiscale method can be greatly improved.

关键词： Multiscale method Wind-tunnel measurement Buoyancy flow Pollutant dispersion numerical error analysis

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Loss Function for Deep Learning to Model Dynamical Systems

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IEICE TRANSACTIONS ON INFORMATION AND SYSTEMS 2024年第11期E107D卷 1458-1462页

作者： Yoshida, Takahito Yaguchi, Takaharu Matsubara, Takashi Osaka Univ Grad Sch Engn Sci Toyonaka 5600043 Japan Kobe Univ Grad Sch Syst Informat Kobe 6578501 Japan Hok kaido Univ Grad Sch Informat Sci & Technol Sapporo 0600808 Japan

Accurately simulating physical systems is essential in various fields. In recent years, deep learning has been used to automatically build models of such systems by learning from data. One such method is the neural ordinary differential equation (neural ODE), which treats the output of a neural network as the time derivative of the system states. However, while this and related methods have shown promise, their training strategies still require further development. Inspired by error analysis techniques in numerical analysis while replacing numerical errors with modeling errors, we propose the error-analytic strategy to address this issue. Therefore, our strategy can capture long-term errors and thus improve the accuracy of long-term predictions.

关键词： key deep learning physical system partial differential equation numerical error analysis

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A DISCONTINUOUS GALERKIN PRESSURE CORRECTION SCHEME FOR THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS: STABILITY AND CONVERGENCE

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MATHEMATICS OF COMPUTATION 2022年第336期91卷 1625-1654页

作者： Masri, Rami Liu, Chen Riviere, Beatrice Rice Univ Dept Computat & Appl Math Houston TX 77005 USA Purdue Univ Dept Math W Lafayette IN 47907 USA

A discontinuous Galerkin pressure correction numerical method for solving the incompressible Navier-Stokes equations is formulated and analyzed. We prove unconditional stability of the proposed scheme. Convergence of the discrete velocity is established by deriving a priori error estimates. numerical results verify the convergence rates.

关键词： Discontinuous Galerkin pressure correction incompressible Navier–Stokes equations numerical error analysis

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error analysis of numerical Weyl fractional derivatives in the case of certain Holder continuous functions 14

Error analysis of numerical Weyl fractional derivatives in t...

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14th IEEE/ASME International Conference on Mechatronic and Embedded Systems and Applications (MESA)

作者： Nissila, Juhani Univ Oulu Fac Technol Mechatron & Machine Diagnost Oulu Finland

ISBN: (纸本)9781538646434

The calculation of fractional or integer order derivatives and integrals has been demonstrated to be simple and fast in the frequency domain. It is also the most sensible method if one wishes to calculate derivatives or integrals of periodic signals. In this paper, error analysis is carried out for the numerical algorithm for Weyl fractional derivatives. To derive an upper bound for the numerical error, some knowledge of the smoothness of the signal must be known in advance or it must be estimated. The derived error analysis is tested with sampled functions with known regularity and with real vibration measurements from rotating machines. Compared to previous publications which deal with error analysis of integer order numerical derivatives in the frequency domain using L-2 errors, the result of this paper is in terms of maximum absolute error and it is based on a novel result on the signal's regularity. The general conclusion using either error estimates is the same: the error of numerical Weyl derivatives is bounded by some constant times the sequence length raised to a negative power. The exponent depends on the smoothness of the signal. This contrasts with using difference quotients in numerical differentiation, in which case the error is bounded by a constant times the sequence length raised to a some fixed negative power and the order of the method defines that exponent.

关键词： fractional calculus Weyl fractional derivatives Fourier analysis Holder regularity numerical error analysis

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numerical error analysis with application to transonic propeller aeroacoustics

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COMPUTERS & FLUIDS 2012年 69卷 20-34页

作者： Giauque, A. Ortun, B. Rodriguez, B. Caruelle, B. Off Natl Etud & Rech Aerosp Dept CFD & Aeroacoust F-92322 Chatillon France Off Natl Etud & Rech Aerosp Dept Appl Aerodynam F-92190 Meudon France Airbus Operat SAS Dept Aeroacoust F-31060 Toulouse France

This article investigates numerical error analysis in the aeroacoustic simulation of transonic propellers for transport aircraft. The objective of this work is double-edged: on one hand to assess consistency of noise predictions, and on the other hand to gain understanding of quadrupolar acoustic sources generated by flow discontinuities such as shock waves. The work methodology is based on the comparison of acoustic predictions, made from RANS flowfield solutions through the Ffowcs-Williams and Hawkings (FWH) method, after considering two major parameters: (1) the influence of CFD grid refinement;and (2) the extension of the flow region enclosed by porous FWH surfaces. The effective spatial convergence order is determined by focusing on the acoustic information in the flow. Richardson's extrapolation is proposed as a method to enhance noise predictions without resorting to expensive CFD computations. It is shown that maximum Sound Pressure Levels (SPLs) for the Blade Passing Frequency (BPF) harmonics converge with the extension of the FWH surface, thereby delimiting a volume enclosing the major acoustic production terms radiating in the rotation plane. On the other hand, it is also shown that SPLs off the propeller plane are much more sensitive to background flow inhomogeneities and cannot be computed with precision using a two-step methodology. Finally, using results related to the convergence of maximum SPLs, an attempt is made to directly link the flowfield solution to volume acoustic sources through a brief analysis of Lighthill's acoustic analogy source term. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： CAA Aeroacoustics numerical error analysis Transonic propeller

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Fast High-Resolution Drawing of Algebraic Curves 22

Fast High-Resolution Drawing of Algebraic Curves

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International Symposium on Symbolic and Algebraic Computation (ISSAC)

作者： Mudiyanselage, Nuwan Herath Moroz, Guillaume Pouget, Marc Univ Lorraine CNRS INRIA LORIA Nancy France

ISBN: (纸本)9781450386883

We address the problem of computing a drawing of high resolution of a plane curve defined by a bivariate polynomial equation p (x,y) = 0. Given a grid of fixed resolution, a drawing is a subset of pixels. Our goal is to compute an approximate drawing that (i) contains all the parts of the curve that intersect the pixel edges, (ii) excludes a pixel when the evaluation of.. with interval arithmetic on each of its four edges is far from zero. One of the challenges forc omputing drawings on a high-resolution grid is to minimize the complexity due to the evaluation of the input polynomial. Most state-of-the-art approaches focus on bounding the number of independent evaluations. Using state-of-the-art Computer Algebra techniques, we design new algorithms that amortize the evaluations and improve the complexity for computing such drawings. Our main contribution is to use a non-uniform grid based on the Chebyshev nodes to take advantage of multipoint evaluation techniques via the Discrete Cosine Transform. We propose two new algorithms that compute drawings and compare them experimentally on several classes of high degree polynomials. Notably, one of those approaches is faster than state-of-the-art drawing software.

关键词： curve drawing high degree algebraic curve discrete cosine transform numerical error analysis fast multipoint evaluation

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Tight error analysis in Fixed-point Arithmetic

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FORMAL ASPECTS OF COMPUTING 2022年第1期34卷 3-3页

作者： Simic, Stella Bemporad, Alberto Inverso, Omar Tribastone, Mirco IMT Sch Adv Studies Lucca Italy Gran Sasso Sci Inst Laquila Italy

We consider the problem of estimating the numerical accuracy of programs with operations in fixed-point arithmetic and variables of arbitrary, mixed precision, and possibly non-deterministic value. By applying a set of parameterised rewrite rules, we transform the relevant fragments of the program under consideration into sequences of operations in integer arithmetic over vectors of bits, thereby reducing the problem as to whether the error enclosures in the initial program can ever exceed a given order of magnitude to simple reachability queries on the transformed program. We describe a possible verification flow and a prototype analyser that implements our technique. We present an experimental evaluation on a particularly complex industrial case study, including a preliminary comparison between bit-level and word-level decision procedures.

关键词： Fixed-point arithmetic static analysis numerical error analysis program transformation

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Tight error analysis in Fixed-Point Arithmetic 16th

Tight Error Analysis in Fixed-Point Arithmetic

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16th International Conference on Integrated Formal Methods (IFM)

作者： Simic, Stella Bemporad, Alberto Inverso, Omar Tribastone, Mirco IMT Sch Adv Studies Lucca Italy Gran Sasso Sci Inst Laquila Italy

ISBN: (纸本)9783030634612;9783030634605

We consider the problem of estimating the numerical accuracy of programs with operations in fixed-point arithmetic and variables of arbitrary, mixed precision and possibly non-deterministic value. By applying a set of parameterised rewrite rules, we transform the relevant fragments of the program under consideration into sequences of operations in integer arithmetic over vectors of bits, thereby reducing the problem as to whether the error enclosures in the initial program can ever exceed a given order of magnitude to simple reachability queries on the transformed program. We present a preliminary experimental evaluation of our technique on a particularly complex industrial case study.

关键词： Fixed-point arithmetic Static analysis numerical error analysis Program transformation

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Quantifying Sub-gridding errors in Standard and Hybrid Higher Order 2D FDTD Simulations

Quantifying Sub-gridding Errors in Standard and Hybrid Highe...

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International Symposium of Applied-Computational-Electromagnetics-Society (ACES)

作者： Le, Madison Hadi, Mohammed Elsherbeni, Atef Colorado Sch Mines Elect Engn Dept Golden CO 80401 USA

ISBN: (纸本)9781733509602

Sub-gridding errors for a 2D Finite-Difference Time-Domain (FDTD) simulation are compared for both the standard FDTD and Hybrid higher order FDTD cases. Sub-gridding contrast ratios of 1:3, 1:9, 1:15, and 1:27 are considered and analyzed. A correlation is seen between the increase of contrast ratio with the increase of sub-gridding errors for both standard and hybrid cases. However, a trend of errors reduction when using hybrid formulations over standard formulations. is apparent for each contrast ratio.

关键词： Finite-Difference Time-Domain Method High Order FDTD numerical error analysis Sub-gridding

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Quantifying Subgridding errors when Modeling Multiscale Structures with FDTD

Quantifying Subgridding Errors when Modeling Multiscale Stru...

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International Symposium of Applied-Computational-Electromagnetics-Society (ACES)

作者： Le, Madison Hadi, Mohammed Elsherbeni, Atef Colorado Sch Mines Elect Engn Dept Golden CO 80401 USA

ISBN: (纸本)9780996007887

This paper discusses the growing subgridding errors in Finite-Difference Time-Domain (FDTD) analysis when applied on electrically large subgrids. FDTD simulations in 1D and 2D spaces are used with a 1:3 contrast ratio. error levels are found to be linearly proportional to the subgrid's electrical dimension along the wave's propagation path. This linear growth suggests numerical phase error mismatch between coarse and fine grids as the subgridding error source.

关键词： Finite-difference time-domain method numerical error analysis subgridding multi-scale problems

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