Journal of Computational Physics: X最新文献_第2页

The 3D Elliptical Parcel-In-Cell (EPIC) method 三维椭圆单元包(EPIC)方法

Journal of Computational Physics: X Pub Date : 2023-11-01 Epub Date: 2023-11-15 DOI: 10.1016/j.jcpx.2023.100136

Matthias Frey , David Dritschel , Steven Böing

{"title":"The 3D Elliptical Parcel-In-Cell (EPIC) method","authors":"Matthias Frey , David Dritschel , Steven Böing","doi":"10.1016/j.jcpx.2023.100136","DOIUrl":"https://doi.org/10.1016/j.jcpx.2023.100136","url":null,"abstract":"<div><p>We present the three-dimensional version of the Elliptical Parcel-In-Cell (EPIC) method for the simulation of fluid flows and analogous continuum systems. The method represents a flow using a space-filling set of ellipsoidal parcels, which move, rotate and deform in the flow field. Additionally, parcels may carry any number of attributes, such as vorticity, density, temperature, etc, which generally evolve in time on the moving parcels. An underlying grid is used for efficiency in computing the velocity field from the interpolated vorticity field, and in obtaining parcel attribute tendencies. Mixing is enabled by permitting parcels to split when excessively deformed, and by merging very small parcels with the nearest other parcel. Several tests are provided which illustrate the behaviour of the method and demonstrate its effectiveness in modelling complex, buoyancy-driven turbulent fluid flows. The results are compared with a large eddy simulation (LES) and a direct numerical simulation (DNS) model.</p></div>","PeriodicalId":37045,"journal":{"name":"Journal of Computational Physics: X","volume":"17 ","pages":"Article 100136"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2590055223000148/pdfft?md5=b80b927c5faff1329ce80f89f5b41be0&pid=1-s2.0-S2590055223000148-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138413547","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

A conformal mapping approach to modelling two-dimensional stratified flow 二维分层流建模的保角映射方法

Journal of Computational Physics: X Pub Date : 2023-11-01 Epub Date: 2023-06-02 DOI: 10.1016/j.jcpx.2023.100129

Heidi J. Dritschel , David G. Dritschel , Magda Carr

{"title":"A conformal mapping approach to modelling two-dimensional stratified flow","authors":"Heidi J. Dritschel , David G. Dritschel , Magda Carr","doi":"10.1016/j.jcpx.2023.100129","DOIUrl":"https://doi.org/10.1016/j.jcpx.2023.100129","url":null,"abstract":"<div><p>Herein we describe a new approach to modelling inviscid two-dimensional stratified flows in a general domain. The approach makes use of a conformal map of the domain to a rectangle. In this transformed domain, the equations of motion are largely unaltered, and in particular Laplace's equation remains unchanged. This enables one to construct exact solutions to Laplace's equation and thereby enforce all boundary conditions.</p><p>An example is provided for two-dimensional flow under the Boussinesq approximation, though the approach is much more general (albeit restricted to two-dimensions). This example is motivated by flow under a weir in a tidal estuary. Here, we discuss how to use a dynamically-evolving conformal map to model changes in the water height on either side of the weir, though the example presented keeps these heights fixed due to limitations in the computational speed to generate the conformal map.</p><p>The numerical approach makes use of contour advection, wherein material buoyancy contours are advected conservatively by the local fluid velocity, while a dual contour-grid representation is used for the vorticity in order to account for vorticity generation from horizontal buoyancy gradients. This generation is accurately estimated by using the buoyancy contours directly, rather than a gridded version of the buoyancy field. The result is a highly-accurate, efficient numerical method with extremely low levels of numerical damping.</p></div>","PeriodicalId":37045,"journal":{"name":"Journal of Computational Physics: X","volume":"17 ","pages":"Article 100129"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50191213","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Efficient variable cell shape geometry optimization 高效的可变单元格形状几何优化

Journal of Computational Physics: X Pub Date : 2023-11-01 Epub Date: 2023-07-25 DOI: 10.1016/j.jcpx.2023.100131

Moritz Gubler, Marco Krummenacher, Hannes Huber, Stefan Goedecker

引用次数: 2

Discontinuous Galerkin spectral element method for shock capturing with summation by parts properties 具有零件性质求和的冲击捕获的间断Galerkin谱元方法

Journal of Computational Physics: X Pub Date : 2023-11-01 Epub Date: 2023-01-06 DOI: 10.1016/j.jcpx.2023.100123

Fengrui Zhang, Yulia T. Peet

{"title":"Discontinuous Galerkin spectral element method for shock capturing with summation by parts properties","authors":"Fengrui Zhang, Yulia T. Peet","doi":"10.1016/j.jcpx.2023.100123","DOIUrl":"https://doi.org/10.1016/j.jcpx.2023.100123","url":null,"abstract":"<div><p>This paper presents a computational methodology developed for a high-order approximation of compressible fluid dynamics equations with discontinuities. The methodology is based on a discontinuous Galerkin spectral-element method (DGSEM) built upon a split discretization framework with summation-by-parts (SBP) property, which mimics the integration-by-parts operation in a discrete sense. To extend the split DGSEM framework to discontinuous cases, we implement a shock capturing method based on the entropy viscosity formulation. The developed high-order split-form DGSEM with shock-capturing methodology is subject to a series of evaluation on both one-dimensional and two-dimensional, continuous and discontinuous cases. Convergence of the method is demonstrated both for smooth and shocked cases that have analytical solutions. The 2D Riemann problem tests illustrate an accurate representation of all the relevant flow phenomena, such as shocks, contact discontinuities, and rarefaction waves. All test cases are able to run with a polynomial order of 7 or higher. The values of the tunable parameters related to the entropy viscosity are robust for both 1D and 2D test problems. We also show that higher-order approximations yield smaller errors than lower-order approximations, for the same number of total degrees of freedom.</p></div>","PeriodicalId":37045,"journal":{"name":"Journal of Computational Physics: X","volume":"17 ","pages":"Article 100123"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50191204","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Bayesian deep learning for partial differential equation parameter discovery with sparse and noisy data 基于贝叶斯深度学习的稀疏噪声数据偏微分方程参数发现

Journal of Computational Physics: X Pub Date : 2022-09-01 Epub Date: 2022-09-29 DOI: 10.1016/j.jcpx.2022.100115

Christophe Bonneville , Christopher Earls

{"title":"Bayesian deep learning for partial differential equation parameter discovery with sparse and noisy data","authors":"Christophe Bonneville , Christopher Earls","doi":"10.1016/j.jcpx.2022.100115","DOIUrl":"https://doi.org/10.1016/j.jcpx.2022.100115","url":null,"abstract":"<div><p>Scientific machine learning has been successfully applied to inverse problems and PDE discovery in computational physics. One caveat concerning current methods is the need for large amounts of (“clean”) data, in order to characterize the full system response and discover underlying physical models. Bayesian methods may be particularly promising for overcoming these challenges, as they are naturally less sensitive to the negative effects of sparse and noisy data. In this paper, we propose to use Bayesian neural networks (BNN) in order to: 1) Recover the full system states from measurement data (e.g. temperature, velocity field, etc.). We use Hamiltonian Monte-Carlo to sample the posterior distribution of a deep and dense BNN, and show that it is possible to accurately capture physics of varying complexity, without overfitting. 2) Recover the parameters instantiating the underlying partial differential equation (PDE) governing the physical system. Using the trained BNN, as a surrogate of the system response, we generate datasets of derivatives that are potentially comprising the latent PDE governing the observed system and then perform a sequential threshold Bayesian linear regression (STBLR), between the successive derivatives in space and time, to recover the original PDE parameters. We take advantage of the confidence intervals within the BNN outputs, and introduce the spatial derivatives cumulative variance into the STBLR likelihood, to mitigate the influence of highly uncertain derivative data points; thus allowing for more accurate parameter discovery. We demonstrate our approach on a handful of example, in applied physics and non-linear dynamics.</p></div>","PeriodicalId":37045,"journal":{"name":"Journal of Computational Physics: X","volume":"16 ","pages":"Article 100115"},"PeriodicalIF":0.0,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2590055222000117/pdfft?md5=74e974fee9a03ffefb4197fc6a8e312b&pid=1-s2.0-S2590055222000117-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72263793","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 8

Increasing stable time-step sizes of the free-surface problem arising in ice-sheet simulations 增加冰盖模拟中自由表面问题的稳定时间步长

Journal of Computational Physics: X Pub Date : 2022-09-01 Epub Date: 2022-08-25 DOI: 10.1016/j.jcpx.2022.100114

André Löfgren , Josefin Ahlkrona , Christian Helanow

{"title":"Increasing stable time-step sizes of the free-surface problem arising in ice-sheet simulations","authors":"André Löfgren , Josefin Ahlkrona , Christian Helanow","doi":"10.1016/j.jcpx.2022.100114","DOIUrl":"https://doi.org/10.1016/j.jcpx.2022.100114","url":null,"abstract":"<div><p>Numerical models for predicting future ice mass loss of the Antarctic and Greenland ice sheets require accurately representing their dynamics. Unfortunately, ice-sheet models suffer from a very strict time-step size constraint, which for higher-order models constitutes a severe bottleneck; in each time step a nonlinear and computationally demanding system of equations has to be solved. In this study, stable time-step sizes are increased for a full-Stokes model by implementing a so-called free-surface stabilization algorithm (FSSA). Previously this stabilization has been used successfully in mantle-convection simulations where a similar viscous-flow problem is solved. By numerical investigation it is demonstrated that instabilities on the very thin domains required for ice-sheet modeling behave differently than on the equal-aspect-ratio domains the stabilization has previously been used on. Despite this, and despite the different material properties of ice, it is shown that it is possible to adapt FSSA to work on idealized ice-sheet domains and increase stable time-step sizes by at least one order of magnitude. The FSSA method presented is deemed accurate, efficient and straightforward to implement into existing ice-sheet solvers.</p></div>","PeriodicalId":37045,"journal":{"name":"Journal of Computational Physics: X","volume":"16 ","pages":"Article 100114"},"PeriodicalIF":0.0,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2590055222000105/pdfft?md5=2969aa66f82dfb99d2673c785b1011c8&pid=1-s2.0-S2590055222000105-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72270229","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3

FC-based shock-dynamics solver with neural-network localized artificial-viscosity assignment 基于FC的神经网络局部人工粘度分配冲击动力学求解器

Journal of Computational Physics: X Pub Date : 2022-06-01 Epub Date: 2022-06-09 DOI: 10.1016/j.jcpx.2022.100110

Oscar P. Bruno , Jan S. Hesthaven , Daniel V. Leibovici

{"title":"FC-based shock-dynamics solver with neural-network localized artificial-viscosity assignment","authors":"Oscar P. Bruno , Jan S. Hesthaven , Daniel V. Leibovici","doi":"10.1016/j.jcpx.2022.100110","DOIUrl":"https://doi.org/10.1016/j.jcpx.2022.100110","url":null,"abstract":"<div><p>This paper presents a spectral scheme for the numerical solution of nonlinear conservation laws in <em>non-periodic domains under arbitrary boundary conditions</em>. The approach relies on the use of the Fourier Continuation (FC) method for spectral representation of non-periodic functions in conjunction with smooth localized artificial viscosity assignments produced by means of a Shock-Detecting Neural Network (SDNN). Like previous shock capturing schemes and artificial viscosity techniques, the combined FC-SDNN strategy effectively controls spurious oscillations in the proximity of discontinuities. Thanks to its use of a <em>localized but smooth artificial viscosity term</em>, whose support is restricted to a vicinity of flow-discontinuity points, the algorithm enjoys spectral accuracy and low dissipation away from flow discontinuities, and, in such regions, it produces smooth numerical solutions—as evidenced by an essential absence of spurious oscillations in level set lines. The FC-SDNN viscosity assignment, which does not require use of problem-dependent algorithmic parameters, induces a significantly lower overall dissipation than other methods, including the Fourier-spectral versions of the previous entropy viscosity method. The character of the proposed algorithm is illustrated with a variety of numerical results for the linear advection, Burgers and Euler equations in one and two-dimensional non-periodic spatial domains.</p></div>","PeriodicalId":37045,"journal":{"name":"Journal of Computational Physics: X","volume":"15 ","pages":"Article 100110"},"PeriodicalIF":0.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2590055222000063/pdfft?md5=84cb83e76e3e7810c4466965c4078ca4&pid=1-s2.0-S2590055222000063-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72263792","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 6

EPIC: The Elliptical Parcel-In-Cell method EPIC：细胞内椭圆包裹法

Journal of Computational Physics: X Pub Date : 2022-03-01 Epub Date: 2022-06-06 DOI: 10.1016/j.jcpx.2022.100109

Matthias Frey , David Dritschel , Steven Böing

{"title":"EPIC: The Elliptical Parcel-In-Cell method","authors":"Matthias Frey , David Dritschel , Steven Böing","doi":"10.1016/j.jcpx.2022.100109","DOIUrl":"https://doi.org/10.1016/j.jcpx.2022.100109","url":null,"abstract":"<div><p>We present a novel approach to simulating general two-dimensional flows, which could also be applied to other areas of continuum mechanics. The approach generalises the Particle-In-Cell (PIC) method, originally used to model two-dimensional hydrodynamics, by representing fluid elements by elliptical parcels. The rotation and deformation of these parcels are calculated, and parcels split beyond a critical aspect ratio. Conversely, small parcels are eliminated by merging them with larger ones. The elliptical parcels well represent the flow deformation and have excellent conservation properties. In contrast to earlier work that combined PIC with elliptical parcels that split and merge, a vorticity-based framework is used, and accurate integration over ellipses is performed efficiently by two-point Gaussian quadrature. The small-scale mixing associated with parcel splitting and merging is shown to be strongly convergent with grid resolution. The robustness, versatility, accuracy and efficiency of the new Elliptical Parcel-In-Cell (EPIC) method is demonstrated for a variety of standard test cases, and compared with a standard pseudo-spectral method. The results indicate that EPIC is a promising, Lagrangian-based alternative to grid-based methods.</p></div>","PeriodicalId":37045,"journal":{"name":"Journal of Computational Physics: X","volume":"14 ","pages":"Article 100109"},"PeriodicalIF":0.0,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2590055222000051/pdfft?md5=41ecceabd534f12f6aa69318f63a6197&pid=1-s2.0-S2590055222000051-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72232766","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3

Hierarchical regularization of solution ambiguity in underdetermined inverse and optimization problems 欠定逆和优化问题解模糊性的层次正则化

Journal of Computational Physics: X Pub Date : 2022-01-01 Epub Date: 2022-03-28 DOI: 10.1016/j.jcpx.2022.100105

Robert Epp , Franca Schmid , Patrick Jenny

{"title":"Hierarchical regularization of solution ambiguity in underdetermined inverse and optimization problems","authors":"Robert Epp , Franca Schmid , Patrick Jenny","doi":"10.1016/j.jcpx.2022.100105","DOIUrl":"https://doi.org/10.1016/j.jcpx.2022.100105","url":null,"abstract":"<div><p>Estimating modeling parameters based on a prescribed optimization target requires to solve an inverse problem, which is commonly ill-posed. Consequently, either infinitely many or no solutions may exist, depending on whether the system is under- or overdetermined, and whether it is consistent or inconsistent. This paper focuses on scenarios where the solution is ambiguous and infinitely many combinations of possible parameter values can accurately achieve the optimization target. Selecting the most suitable solution requires incorporating additional constraints into the model, which is achieved by regularizing the inverse problem. However, common regularization approaches require the specification of <em>a priori</em> unknown regularization hyperparameters that are difficult and tedious to obtain, and can have a large impact on the result.</p><p>Here, a novel strategy to reduce the ambiguity of such inverse problems is presented, ensuring that the primary optimization target is always reached accurately. To further reduce the solution space, additional constraints are included, until the optimal modeling parameters are found. Importantly, the required regularization parameters have a direct physical meaning and can be derived sequentially, starting from an initial guess that can be obtained conveniently by solving the system without regularization.</p><p>By considering several illustrative examples, the applicability of the method is demonstrated, and its potential for various comparable inverse problems is highlighted.</p></div>","PeriodicalId":37045,"journal":{"name":"Journal of Computational Physics: X","volume":"13 ","pages":"Article 100105"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2590055222000014/pdfft?md5=ab832516badf36d8094a3864889c559f&pid=1-s2.0-S2590055222000014-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72232765","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

A recursive system-free single-step temporal discretization method for finite difference methods 有限差分方法的递归无系统单步时间离散化方法

Journal of Computational Physics: X Pub Date : 2021-09-01 Epub Date: 2021-07-02 DOI: 10.1016/j.jcpx.2021.100098

Youngjun Lee , Dongwook Lee , Adam Reyes

{"title":"A recursive system-free single-step temporal discretization method for finite difference methods","authors":"Youngjun Lee , Dongwook Lee , Adam Reyes","doi":"10.1016/j.jcpx.2021.100098","DOIUrl":"https://doi.org/10.1016/j.jcpx.2021.100098","url":null,"abstract":"<div><p>Single-stage or single-step high-order temporal discretizations of partial differential equations (PDEs) have shown great promise in delivering high-order accuracy in time with efficient use of computational resources. There has been much success in developing such methods for finite volume method (FVM) discretizations of PDEs. The Picard Integral formulation (PIF) has recently made such single-stage temporal methods accessible for finite difference method (FDM) discretizations. PIF methods rely on the so-called Lax-Wendroff procedures to tightly couple spatial and temporal derivatives through the governing PDE system to construct high-order Taylor series expansions in time. Going to higher than third order in time requires the calculation of <em>Jacobian-like</em> derivative tensor-vector contractions of an increasingly larger degree, greatly adding to the complexity of such schemes. To that end, we present in this paper a method for calculating these tensor contractions through a recursive application of a discrete Jacobian operator that readily and efficiently computes the needed contractions entirely agnostic of the system of partial differential equations (PDEs) being solved.</p></div>","PeriodicalId":37045,"journal":{"name":"Journal of Computational Physics: X","volume":"12 ","pages":"Article 100098"},"PeriodicalIF":0.0,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jcpx.2021.100098","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72266797","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1