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Ghost-Fluid-Based Sharp Interface Methods for Multi-Material Dynamics: A Review 基于鬼流体的多材料动力学锐界面方法综述
3区 物理与天体物理 Q1 PHYSICS, MATHEMATICAL Pub Date : 2023-06-01 DOI: 10.4208/cicp.re-2022-0189
Liang Xu null, Tiegang Liu
. The ghost fluid method (GFM) provides a simple way to simulate the interaction of immiscible materials. Especially, the modified GFM (MGFM) and its variants, based on the solutions of multi-material Riemann problems, are capable of faithfully taking into account the effects of nonlinear wave interaction and material property near the interface. Reasonable treatments for ghost fluid states or interface conditions have been shown to be crucial when applied to various interfacial phenomena involving large discontinuity and strong nonlinearity. These methods, therefore, have great potential in engineering applications. In this paper, we review the development of such methods. The methodologies of representative GFM-based algorithms for definition of interface conditions are illustrated and compared to each other. The research progresses in design principle and accuracy analysis are briefly described. Some steps and techniques for multi-dimensional extension are also summarized. In addition, we present some progresses in more challenging scientific problems, including a variety of fluid/solid-fluid/solid interactions with complex physical properties. Of course the challenges faced by researchers in this field are also discussed.
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引用次数: 0
A Stable Arbitrarily High Order Time-Stepping Method for Thermal Phase Change Problems 热相变问题的稳定任意高阶时间步进方法
IF 3.7 3区 物理与天体物理 Q1 PHYSICS, MATHEMATICAL Pub Date : 2023-06-01 DOI: 10.4208/cicp.oa-2022-0183
Wei Wang null, Chuanju Xu
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引用次数: 0
High-Order Local Discontinuous Galerkin Method with Multi-Resolution WENO Limiter for Navier-Stokes Equations on Triangular Meshes 三角网格上Navier-Stokes方程的高阶局部不连续Galerkin方法
IF 3.7 3区 物理与天体物理 Q1 PHYSICS, MATHEMATICAL Pub Date : 2023-06-01 DOI: 10.4208/cicp.oa-2022-0096
Yizhou Lu, Jun Zhu, S. Cui, Zhenming Wang, Linlin Tian null, N. Zhao
. In this paper, a new multi-resolution weighted essentially non-oscillatory (MR-WENO) limiter for high-order local discontinuous Galerkin (LDG) method is designed for solving Navier-Stokes equations on triangular meshes. This MR-WENO limiter is a new extension of the finite volume MR-WENO schemes. Such new limiter uses information of the LDG solution essentially only within the troubled cell itself, to build a sequence of hierarchical L 2 projection polynomials from zeroth degree to the highest degree of the LDG method. As an example, a third-order LDG method with associated same order MR-WENO limiter has been developed in this paper, which could maintain the original order of accuracy in smooth regions and could simultaneously suppress spurious oscillations near strong shocks or contact discontinuities. The linear weights of such new MR-WENO limiter can be any positive numbers on condition that their summation is one. This is the first time that a series
. 针对三角网格上求解Navier-Stokes方程的高阶局部不连续Galerkin方法,设计了一种新的多分辨率加权本质非振荡(MR-WENO)限幅器。该MR-WENO限制器是有限体积MR-WENO方案的新扩展。这种新的限制器基本上只使用LDG解在问题单元本身的信息,来构建LDG方法从0次到最高次的分层l2投影多项式序列。作为一个例子,本文提出了一种带有同阶MR-WENO限制器的三阶LDG方法,该方法可以在光滑区域保持原阶精度,同时可以抑制强冲击或接触不连续附近的杂散振荡。这种新的MR-WENO限制器的线性权可以是任意正数,条件是它们的和为1。这是第一次一个系列
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引用次数: 0
A Correction and Comments on “Multi-Scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains CiCP, 28(5):1970–2001,2020” 对“求解复域Poisson-Boltzmann方程的多尺度深度神经网络(MscaleDNN)”的修正和评论CiCP,28(5):1970–20012020
IF 3.7 3区 物理与天体物理 Q1 PHYSICS, MATHEMATICAL Pub Date : 2023-06-01 DOI: 10.4208/cicp.oa-2023-0152
Lulu Zhang, Wei Cai null, Z. Xu
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引用次数: 1
Sixth-Order Compact Finite Difference Method for 2D Helmholtz Equations with Singular Sources and Reduced Pollution Effect 具有奇异源和减少污染效应的二维Helmholtz方程的六阶紧致有限差分方法
3区 物理与天体物理 Q1 PHYSICS, MATHEMATICAL Pub Date : 2023-06-01 DOI: 10.4208/cicp.oa-2023-0062
Qiwei Feng, Bin Han null, Michelle Michelle
Due to its highly oscillating solution, the Helmholtz equation is numerically challenging to solve. To obtain a reasonable solution, a mesh size that is much smaller than the reciprocal of the wavenumber is typically required (known as the pollution effect). High order schemes are desirable, because they are better in mitigating the pollution effect. In this paper, we present a high order compact finite difference method for 2D Helmholtz equations with singular sources, which can also handle any possible combinations of boundary conditions (Dirichlet, Neumann, and impedance) on a rectangular domain. Our method achieves a sixth order consistency for a constant wavenumber, and a fifth order consistency for a piecewise constant wavenumber. To reduce the pollution effect, we propose a new pollution minimization strategy that is based on the average truncation error of plane waves. Our numerical experiments demonstrate the superiority of our proposed finite difference scheme with reduced pollution effect to several state-of-the-art finite difference schemes, particularly in the critical pre-asymptotic region where $textsf{k} h$ is near $1$ with $textsf{k}$ being the wavenumber and $h$ the mesh size.
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引用次数: 3
Adaptive Ensemble Kalman Inversion with Statistical Linearization 统计线性化自适应集合卡尔曼反演
IF 3.7 3区 物理与天体物理 Q1 PHYSICS, MATHEMATICAL Pub Date : 2023-06-01 DOI: 10.4208/cicp.oa-2023-0012
Yanyan Wang, Qiang Li null, Liang Yan
. The ensemble Kalman inversion (EKI), inspired by the well-known ensemble Kalman filter, is a derivative-free and parallelizable method for solving inverse problems. The method is appealing for applications in a variety of fields due to its low computational cost and simple implementation. In this paper, we propose an adaptive ensemble Kalman inversion with statistical linearization (AEKI-SL) method for solving inverse problems from a hierarchical Bayesian perspective. Specifically, by adaptively updating the unknown with an EKI and updating the hyper-parameter in the prior model, the method can improve the accuracy of the solutions to the inverse problem. To avoid semi-convergence, we employ Morozov’s discrepancy principle as a stopping criterion. Furthermore, we extend the method to simultaneous estimation of noise levels in order to reduce the randomness of artificially ensemble noise levels. The convergence of the hyper-parameter in prior model is investigated theoretically. Numerical experiments show that our proposed methods outperform the traditional EKI and EKI with statistical linearization (EKI-SL) methods.
. 集合卡尔曼反演(EKI)是一种求解逆问题的无导数、可并行化的方法,其灵感来源于著名的集合卡尔曼滤波。该方法具有计算成本低、实现简单等优点,具有广泛的应用前景。本文从层次贝叶斯的角度出发,提出了一种统计线性化自适应集合卡尔曼反演(AEKI-SL)方法。具体而言,该方法通过自适应地更新EKI和更新先验模型中的超参数,提高了反问题解的精度。为了避免半收敛,我们采用Morozov的差异原理作为停止判据。此外,我们将该方法扩展到同时估计噪声级,以降低人工集合噪声级的随机性。从理论上研究了先验模型中超参数的收敛性。数值实验表明,本文提出的方法优于传统的EKI方法和统计线性化EKI方法。
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引用次数: 0
Adaptive Multi-Resolution Method for 3D Reactive Flows with Level Set Front Capturing 具有水平集前沿捕获的三维反应流自适应多分辨率方法
IF 3.7 3区 物理与天体物理 Q1 PHYSICS, MATHEMATICAL Pub Date : 2023-06-01 DOI: 10.4208/cicp.oa-2022-0122
Wenhua Ma, Dongmi Luo, W. Ying, Guoxi Ni, M. null, Yibing Chen
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引用次数: 0
Quantum Implementation of Numerical Methods for Convection-Diffusion Equations: Toward Computational Fluid Dynamics 对流扩散方程数值方法的量子实现:走向计算流体动力学
IF 3.7 3区 物理与天体物理 Q1 PHYSICS, MATHEMATICAL Pub Date : 2023-06-01 DOI: 10.4208/cicp.oa-2022-0081
Bofeng Liu, Lixing Zhu, Zixuan Yang null, Guowei He
{"title":"Quantum Implementation of Numerical Methods for Convection-Diffusion Equations: Toward Computational Fluid Dynamics","authors":"Bofeng Liu, Lixing Zhu, Zixuan Yang null, Guowei He","doi":"10.4208/cicp.oa-2022-0081","DOIUrl":"https://doi.org/10.4208/cicp.oa-2022-0081","url":null,"abstract":"","PeriodicalId":50661,"journal":{"name":"Communications in Computational Physics","volume":" ","pages":""},"PeriodicalIF":3.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41472907","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Frozen Gaussian Approximation for the Dirac Equation in Curved Space with Application to Strained Graphene Dirac方程在弯曲空间中的冻结高斯逼近及其在应变石墨烯中的应用
IF 3.7 3区 物理与天体物理 Q1 PHYSICS, MATHEMATICAL Pub Date : 2023-06-01 DOI: 10.4208/cicp.oa-2021-0209
L. Chai, Lorin Emmanuel null, Xu Yang
{"title":"Frozen Gaussian Approximation for the Dirac Equation in Curved Space with Application to Strained Graphene","authors":"L. Chai, Lorin Emmanuel null, Xu Yang","doi":"10.4208/cicp.oa-2021-0209","DOIUrl":"https://doi.org/10.4208/cicp.oa-2021-0209","url":null,"abstract":"","PeriodicalId":50661,"journal":{"name":"Communications in Computational Physics","volume":" ","pages":""},"PeriodicalIF":3.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46271065","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Analysis of Discontinuity Detectors and Hybrid WCNS Schemes Based on Waveform Recognition 基于波形识别的不连续检测器和混合WCNS方案分析
IF 3.7 3区 物理与天体物理 Q1 PHYSICS, MATHEMATICAL Pub Date : 2023-06-01 DOI: 10.4208/cicp.oa-2023-0080
Hao Zhang, Yidao Dong, Shichao Zheng null, Xiaogang Deng
. In this paper, we present a hybrid form of weighted compact nonlinear scheme (WCNS) for hyperbolic conservation laws by applying linear and nonlinear methods for smooth and discontinuous zones individually. To fulfill this algorithm, it is inseparable from the recognition ability of the discontinuity detector adopted. In specific, a troubled-cell indicator is utilized to recognize unsmooth areas such as shock waves and contact discontinuities, while avoiding misjudgments of smooth structures. Some classical detectors are classified into three basic types: derivative combination, smoothness indicators and characteristic decomposition. Meanwhile, a new improved detector is proposed for comparison. Then they are analyzed through identifying a series of waveforms firstly. After that, hybrid schemes using such indicators, as well as different detection variables, are examined with Euler equations, so as to investigate their ability to distinguish practical discontinuities on various levels. Simulation results demonstrate that the proposed algorithm has similar performances to pure WCNS, while it generally saves 50 percent of CPU time for 1D cases and about 40 percent for 2D Euler equations. Current research is in the hope of providing some reference and establishing some standards for judging existing discontinuity detectors and developing novel ones.
在本文中,我们分别应用线性和非线性方法对光滑和不连续区域,提出了双曲守恒律的加权紧致非线性格式(WCNS)的混合形式。要实现该算法,离不开所采用的不连续检测器的识别能力。具体而言,故障单元指示器用于识别不平滑区域,如冲击波和接触不连续性,同时避免对平滑结构的误判。一些经典的检测器分为三种基本类型:导数组合、光滑度指标和特征分解。同时,提出了一种新的改进检测器进行比较。然后通过识别一系列波形对其进行分析。之后,使用欧拉方程对使用这些指标以及不同检测变量的混合方案进行了检验,以研究它们在不同水平上区分实际不连续性的能力。仿真结果表明,该算法具有与纯WCNS相似的性能,而对于1D情况,该算法通常节省50%的CPU时间,对于2D Euler方程,该算法节省约40%的CPU时间。目前的研究希望为判断现有的不连续检测器和开发新的不连续性检测器提供一些参考和建立一些标准。
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引用次数: 0
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Communications in Computational Physics
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