Journal of Computational Physics最新文献_第10页

A three-dimensional curve interface reconstruction algorithm for two-phase fluid flow 两相流体流动的三维曲线界面重构算法

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2024-10-05 DOI: 10.1016/j.jcp.2024.113489

Yujie Chen , Junhua Gong , Dongliang Sun , Dongxu Han , Peng Wang , Bo Yu , Wen-Quan Tao

The curve interface reconstruction algorithm has received significant attention in the context of two-dimensional two-phase flow. However, it remains absent in the three-dimensional scenario. This paper proposes a novel three-dimensional curve interface reconstruction (CIR) algorithm to address this challenge within structured meshes for the first time. Specifically, a portion of the spherical surface is employed to reconstruct the three-dimensional curve interface segment, with the radius and center coordinates determined by curvature and mass conservation constraints, respectively. To enhance curvature accuracy, a sphere-based iterative reconstruction (SIR) algorithm is proposed to calculate the reconstructed distance function (RDF) for the three-dimensional curve interface. Various tests involving the interface reconstruction of spherical, ellipsoidal, and cubic objects demonstrate that the coupled SIR and CIR (SIR-CIR, simplified by SCIR) method achieves higher accuracy than many popular methods, particularly with coarse mesh resolutions. Additionally, the SCIR method offers the advantages of straightforward implementation and coding for interface reconstruction in two-phase flow research. This advantage results in reduced computational costs compared to the coupled volume-of-fluid and level set (VOSET) method, which also utilizes an iterative method to solve RDF.

曲线界面重构算法在二维两相流中受到了极大关注。然而，在三维场景中仍然缺乏这种算法。本文首次提出了一种新型三维曲线界面重建（CIR）算法，以解决结构网格中的这一难题。具体来说，采用球面的一部分来重建三维曲线界面段，半径和中心坐标分别由曲率和质量守恒约束决定。为了提高曲率精度，提出了一种基于球面的迭代重建（SIR）算法，用于计算三维曲线界面的重建距离函数（RDF）。涉及球形、椭圆形和立方体物体界面重建的各种测试表明，耦合 SIR 和 CIR（SIR-CIR，由 SCIR 简化）方法比许多常用方法实现了更高的精度，尤其是在粗网格分辨率下。此外，SCIR 方法还具有在两相流研究中直接实施和编码界面重建的优势。与同样采用迭代法求解 RDF 的流体体积和液面集耦合（VOSET）方法相比，这种优势可降低计算成本。

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引用次数: 0

A staggered Lagrangian magnetohydrodynamics method based on subcell Riemann solver 基于子单元黎曼求解器的交错拉格朗日磁流体力学方法

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2024-10-04 DOI: 10.1016/j.jcp.2024.113479

Xun Wang , Hongping Guo , Zhijun Shen

This paper uses a general formalism to derive staggered Lagrangian method for 2D compressible magnetohydrodynamics (MHD) flows. A subcell method is introduced to discretize the MHD system and some Riemann problems over subcells are solved at the cell center and grid node respectively. In these solvers, only the fast-waves in all jumping relations are considered and thus the solution structure is simple. The discrete conservations of mass, momentum and energy are preserved naturally in the proposed numerical method. In order to meet the thermodynamic Gibbs relation in isentropic flows, an adaptive Riemann solver is implemented at the cell center, in which a criterion is proposed to reduce overheating errors in the rarefying problems and maintains the excellent shock-capturing ability simultaneously. It is worth to be noticed that the divergence-free condition is naturally satisfied in the Lagrangian method. Various numerical tests are presented to demonstrate the accuracy and robustness of the algorithm.

本文采用一般形式主义推导出二维可压缩磁流体动力学（MHD）流的交错拉格朗日方法。本文引入子单元法对 MHD 系统进行离散化，并分别在单元中心和网格节点求解子单元上的一些黎曼问题。在这些求解过程中，只考虑所有跳跃关系中的快波，因此求解结构简单。质量、动量和能量的离散守恒在所提出的数值方法中得到了自然保留。为了满足等熵流中的热力学吉布斯关系，在单元中心实施了自适应黎曼求解器，其中提出了一个标准，以减少稀释问题中的过热误差，并同时保持优异的冲击捕捉能力。值得注意的是，拉格朗日方法自然满足无发散条件。为了证明该算法的准确性和鲁棒性，还进行了各种数值测试。

引用次数: 0

Robustness and reliability of state-space, frame-based modeling for thermoacoustics 基于状态空间和框架的热声建模的鲁棒性和可靠性

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2024-10-04 DOI: 10.1016/j.jcp.2024.113472

Mathieu Cances , Luc Giraud , Michael Bauerheim , Laurent Gicquel , Franck Nicoud

The Galerkin modal expansion is a well-known method used to develop reduced order models for thermoacoustics. A known issue is the appearance of Gibbs-type oscillations on velocity fluctuations at the interface between subdomains and at boundary conditions. Recent work of Laurent et al. (2019) [20] and Laurent et al. (2021) [23] have shown that it is possible to overcome this issue by using an over-completed frame, instead of a Galerkin modal basis. However, the low-order modeling based on this frame modal expansion may generate spurious modes. In this paper, the origin of these non-physical modes is identified and a method is proposed to automatically remove them from the outcome. By preventing any interaction between the physical and non-physical components, the proposed methodology drastically improves the robustness and reliability of the frame modal expansion modeling for thermoacoustics.

Galerkin 模态展开是一种著名的方法，用于开发热声学的降阶模型。一个已知的问题是，在子域之间的界面和边界条件处的速度波动会出现吉布斯型振荡。Laurent 等人（2019 年）[20] 和 Laurent 等人（2021 年）[23] 的最新研究表明，可以通过使用超完成框架而不是 Galerkin 模态基础来克服这一问题。然而，基于这种框架模态展开的低阶建模可能会产生虚假模态。本文确定了这些非物理模态的来源，并提出了一种方法来自动从结果中去除这些模态。通过防止物理成分和非物理成分之间的相互作用，所提出的方法大大提高了热声框架模态展开建模的稳健性和可靠性。

引用次数: 0

Discovering artificial viscosity models for discontinuous Galerkin approximation of conservation laws using physics-informed machine learning 利用物理信息机器学习发现非连续伽勒金近似守恒定律的人工粘度模型

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2024-10-03 DOI: 10.1016/j.jcp.2024.113476

Matteo Caldana, Paola F. Antonietti, Luca Dede'

Finite element-based high-order solvers of conservation laws offer large accuracy but face challenges near discontinuities due to the Gibbs phenomenon. Artificial viscosity is a popular and effective solution to this problem based on physical insight. In this work, we present a physics-informed machine learning algorithm to automate the discovery of artificial viscosity models. We refer to the proposed approach as an “hybrid” approach which stands at the edge between supervised and unsupervised learning. More precisely, the proposed “hybrid” paradigm is not supervised in the classical sense as it does not utilize labeled data in the traditional way but relies on the intrinsic properties of the reference solution. The algorithm is inspired by reinforcement learning and trains a neural network acting cell-by-cell (the viscosity model) by minimizing a loss defined as the difference with respect to a reference solution thanks to automatic differentiation. This enables a dataset-free training procedure. We prove that the algorithm is effective by integrating it into a state-of-the-art Runge-Kutta discontinuous Galerkin solver. We showcase several numerical tests on scalar and vectorial problems, such as Burgers' and Euler's equations in one and two dimensions. Results demonstrate that the proposed approach trains a model that is able to outperform classical viscosity models. Moreover, we show that the learnt artificial viscosity model is able to generalize across different problems and parameters.

基于有限元的高阶守恒定律求解器具有很高的精度，但由于吉布斯现象的存在，在不连续处面临挑战。人工粘度是基于物理洞察力的一种流行而有效的解决方案。在这项工作中，我们提出了一种物理信息机器学习算法，用于自动发现人工粘度模型。我们将所提出的方法称为 "混合 "方法，它处于监督学习和非监督学习之间的边缘。更确切地说，所提出的 "混合 "范式并不是传统意义上的监督学习，因为它并不以传统方式利用标记数据，而是依赖于参考解的内在属性。该算法受到强化学习的启发，通过最小化损失来训练逐个单元行动的神经网络（粘度模型），损失被定义为相对于参考解的差值，这要归功于自动微分。这使得训练过程无需数据集。通过将该算法集成到最先进的 Runge-Kutta 非连续 Galerkin 求解器中，我们证明了该算法的有效性。我们展示了几个标量和矢量问题的数值测试，如一维和二维的布尔格斯方程和欧拉方程。结果表明，所提出的方法训练出的模型能够超越经典粘度模型。此外，我们还表明，学习到的人工粘度模型能够在不同问题和参数之间通用。

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引用次数: 0

On the robustness of high-order upwind summation-by-parts methods for nonlinear conservation laws 论非线性守恒定律的高阶上风逐部求和方法的稳健性

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2024-10-03 DOI: 10.1016/j.jcp.2024.113471

Hendrik Ranocha , Andrew R. Winters , Michael Schlottke-Lakemper , Philipp Öffner , Jan Glaubitz , Gregor J. Gassner

We use the framework of upwind summation-by-parts (SBP) operators developed by Mattsson (2017, doi:10.1016/j.jcp.2017.01.042) and study different flux vector splittings in this context. To do so, we introduce discontinuous-Galerkin-like interface terms for multi-block upwind SBP methods applied to nonlinear conservation laws. We investigate the behavior of the upwind SBP methods for flux vector splittings of varying complexity on Cartesian as well as unstructured curvilinear multi-block meshes. Moreover, we analyze the local linear/energy stability of these methods following Gassner, Svärd, and Hindenlang (2022, doi:10.1007/s10915-021-01720-8). Finally, we investigate the robustness of upwind SBP methods for challenging examples of shock-free flows of the compressible Euler equations such as a Kelvin-Helmholtz instability and the inviscid Taylor-Green vortex.

我们使用 Mattsson（2017，doi:10.1016/j.jcp.2017.01.042）开发的上风逐部求和（SBP）算子框架，并在此背景下研究不同的通量矢量分裂。为此，我们为应用于非线性守恒定律的多块上风 SBP 方法引入了类似于不连续伽勒金的界面项。我们研究了笛卡尔网格和非结构曲线多块网格上不同复杂度的通量矢量分割的上风 SBP 方法的行为。此外，我们还按照 Gassner、Svärd 和 Hindenlang（2022，doi:10.1007/s10915-021-01720-8）的方法分析了这些方法的局部线性/能量稳定性。最后，我们研究了上风 SBP 方法对可压缩欧拉方程无冲击流的挑战性实例（如开尔文-赫姆霍兹不稳定性和不粘性泰勒-格林涡旋）的稳健性。

引用次数: 0

DG-IMEX method for a two-moment model for radiation transport in the O(v/c) limit O(v/c) 极限辐射输运双矩模型的 DG-IMEX 方法

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2024-10-03 DOI: 10.1016/j.jcp.2024.113477

M. Paul Laiu , Eirik Endeve , J. Austin Harris , Zachary Elledge , Anthony Mezzacappa

We consider neutral particle systems described by moments of a phase-space density and propose a realizability-preserving numerical method to evolve a spectral two-moment model for particles interacting with a background fluid moving with nonrelativistic velocities. The system of nonlinear moment equations, with special relativistic corrections to

O (v / c)

, expresses a balance between phase-space advection and collisions and includes velocity-dependent terms that account for spatial advection, Doppler shift, and angular aberration. The model is conservative for the correct

O (v / c)

Eulerian-frame number density and is consistent, to

O (v / c)

, with Eulerian-frame energy and momentum conservation. This model is closely related to the one promoted by Lowrie et al. [1] and similar to models currently used to study transport phenomena in large-scale simulations of astrophysical environments. The proposed numerical method is designed to preserve moment realizability, which guarantees that the moments correspond to a nonnegative phase-space density. The realizability-preserving scheme consists of the following key components: (i) a strong stability-preserving implicit-explicit (IMEX) time-integration method; (ii) a discontinuous Galerkin (DG) phase-space discretization with carefully constructed numerical fluxes; (iii) a realizability-preserving implicit collision update; and (iv) a realizability-enforcing limiter. In time integration, nonlinearity of the moment model necessitates solution of nonlinear equations, which we formulate as fixed-point problems and solve with tailored iterative solvers that preserve moment realizability with guaranteed global convergence. We also analyze the simultaneous Eulerian-frame number and energy conservation properties of the semi-discrete DG scheme and propose a “spectral redistribution” scheme that promotes Eulerian-frame energy conservation. Through numerical experiments, we demonstrate the accuracy and robustness of this DG-IMEX method and investigate its Eulerian-frame energy conservation properties.

我们考虑了由相空间密度矩描述的中性粒子系统，并提出了一种保留可实现性的数值方法，用于演化粒子与以非相对论速度运动的背景流体相互作用的光谱双矩模型。该非线性矩方程系统具有对 O(v/c)的特殊相对论修正，表达了相空间平流和碰撞之间的平衡，并包含了考虑空间平流、多普勒频移和角像差的速度相关项。该模型对于正确的欧拉帧数密度 O(v/c)是保守的，并且与欧拉帧能量和动量守恒在 O(v/c)范围内是一致的。该模型与 Lowrie 等人[1]推广的模型密切相关，并与目前用于研究大规模模拟天体物理环境中的输运现象的模型相似。所提出的数值方法旨在保持力矩的可实现性，从而保证力矩对应于非负的相空间密度。可实现性保留方案由以下关键部分组成：(i) 强稳定性保护隐式-显式（IMEX）时间积分法；(ii) 非连续加勒金（DG）相空间离散化，并精心构建数值通量；(iii) 可实现性保护隐式碰撞更新；(iv) 可实现性强化限制器。在时间积分中，力矩模型的非线性要求非线性方程的求解，我们将其表述为定点问题，并使用量身定制的迭代求解器求解，该求解器可在保证全局收敛的情况下保持力矩可实现性。我们还分析了半离散 DG 方案的同时欧拉帧数和能量守恒特性，并提出了一种促进欧拉帧能量守恒的 "谱再分布 "方案。通过数值实验，我们证明了这种 DG-IMEX 方法的精确性和鲁棒性，并研究了其欧拉帧能量守恒特性。

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引用次数: 0

Well-balanced path-conservative discontinuous Galerkin methods with equilibrium preserving space for two-layer shallow water equations 针对两层浅水方程的具有平衡保留空间的均衡路径保守非连续伽勒金方法

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2024-10-02 DOI: 10.1016/j.jcp.2024.113473

Jiahui Zhang , Yinhua Xia , Yan Xu

This paper introduces well-balanced path-conservative discontinuous Galerkin (DG) methods for two-layer shallow water equations, ensuring exactness for both still water and moving water equilibrium steady states. The approach involves approximating the equilibrium variables within the DG piecewise polynomial space, while expressing the DG scheme in the form of path-conservative schemes. To robustly handle the nonconservative products governing momentum exchange between the layers, we incorporate the theory of Dal Maso, LeFloch, and Murat (DLM) within the DG method. Additionally, linear segment paths connecting the equilibrium functions are chosen to guarantee the well-balanced property of the resulting scheme. The simple “lake-at-rest” steady state is naturally satisfied without any modification, while a specialized treatment of the numerical flux is crucial for preserving the moving water steady state. Extensive numerical examples in one and two dimensions validate the exact equilibrium preservation of the steady state solutions and demonstrate its high-order accuracy. The performance of the method and high-resolution results further underscore its potential as a robust approach for nonconservative hyperbolic balance laws.

本文针对两层浅水方程引入了平衡良好的路径保守非连续伽勒金（DG）方法，确保静水和动水平衡稳态的精确性。该方法涉及在 DG 片断多项式空间内近似平衡变量，同时以路径保守方案的形式表达 DG 方案。为了稳健地处理层间动量交换的非保守乘积，我们在 DG 方法中加入了 Dal Maso、LeFloch 和 Murat（DLM）理论。此外，我们还选择了连接平衡函数的线性分段路径，以保证所产生的方案具有良好的平衡特性。简单的 "湖泊静止 "稳态无需任何修改即可自然得到满足，而数值通量的专门处理对于保持水流运动稳态至关重要。一维和二维的大量数值示例验证了稳态解的精确平衡保持，并证明了其高阶精度。该方法的性能和高分辨率结果进一步凸显了其作为非保守双曲平衡定律稳健方法的潜力。

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引用次数: 0

A transformer-based convolutional method to model inverse cascade in forced two-dimensional turbulence 基于变压器的卷积法模拟强制二维湍流中的逆级联

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2024-10-02 DOI: 10.1016/j.jcp.2024.113475

Haochen Li , Jinhan Xie , Chi Zhang , Yuchen Zhang , Yaomin Zhao

The present work proposes a novel transformer-based convolutional neural network (TransCNN) method to effectively model the inverse energy cascade in two dimensional (2D) turbulence. The TransCNN structure combines large-scale features extracted by transformer with small-scale features from convolutional layers, thus is considered suitable for multi-scale modeling. The novel TransCNN method has been applied to model sub-grid scale (SGS) stress for large-eddy simulation (LES) of 2D turbulence, under the extremely challenging situation that the LES grid is too coarse to resolve the external forcing scale. The data-driven model trained by the novel TransCNN structure is compared to two deep CNN models with varying complexities. All models exhibit proficiency during a priori tests. Notably, TransCNN surpasses its counterparts in predictive accuracy and generalizability in a posteriori tests. An investigation into the receptive fields reveals that the TransCNN model can efficiently leverage global information with the transformer structure, which is key to its superior performance in representing the inverse energy cascade in the 2D turbulent simulations.

本研究提出了一种新颖的基于变压器的卷积神经网络（TransCNN）方法，以有效模拟二维（2D）湍流中的反向能量级联。TransCNN 结构将变压器提取的大尺度特征与卷积层提取的小尺度特征相结合，因此被认为适用于多尺度建模。新颖的 TransCNN 方法已被应用于二维湍流的大涡度模拟（LES）中的子网格尺度（SGS）应力建模，这种情况极具挑战性，因为 LES 网格太粗，无法解析外部强迫尺度。通过新颖的 TransCNN 结构训练的数据驱动模型与两个复杂程度不同的深度 CNN 模型进行了比较。在先验测试中，所有模型都表现出了良好的性能。值得注意的是，在后验测试中，TransCNN 在预测准确性和泛化能力方面超越了同类模型。对感受野的研究表明，TransCNN 模型可以通过变压器结构有效地利用全局信息，这是它在二维湍流模拟中表示反向能量级联方面表现出色的关键所在。

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引用次数: 0

Gradient-enhanced deep Gaussian processes for multifidelity modeling 梯度增强型深度高斯过程用于多保真度建模

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2024-10-02 DOI: 10.1016/j.jcp.2024.113474

Viv Bone, Chris van der Heide, Kieran Mackle, Ingo Jahn, Peter M. Dower, Chris Manzie

Multifidelity models integrate data from multiple sources to produce a single approximator for the underlying process. Dense low-fidelity samples are used to reduce interpolation error, while sparse high-fidelity samples are used to compensate for bias or noise in the low-fidelity samples. Deep Gaussian processes (GPs) are attractive for multifidelity modeling as they are non-parametric, robust to overfitting, perform well for small datasets, and, critically, can capture nonlinear and input-dependent relationships between data of different fidelities. Many datasets naturally contain gradient data, most commonly when they are generated by computational models that have adjoint solutions or are built in automatic differentiation frameworks.

Principally, this work extends deep GPs to incorporate gradient data. We demonstrate this method on an analytical test problem and two realistic aerospace problems: one focusing on a hypersonic waverider with an inviscid gas dynamics truth model and another focusing on the canonical ONERA M6 wing with a viscous Reynolds-averaged Navier-Stokes truth model.

In both examples, the gradient-enhanced deep GP outperforms a gradient-enhanced linear GP model and their non-gradient-enhanced counterparts.

多保真度模型整合了多个来源的数据，为基本过程生成一个近似值。密集的低保真样本用于减少插值误差，而稀疏的高保真样本则用于补偿低保真样本中的偏差或噪声。深度高斯过程（GPs）对多保真度建模很有吸引力，因为它们是非参数的，对过拟合很稳健，对小数据集也有很好的表现，更重要的是，它们可以捕捉不同保真度数据之间的非线性和输入依赖关系。许多数据集自然包含梯度数据，最常见的情况是这些数据集是由具有邻接解的计算模型生成的，或者是在自动微分框架中构建的。我们在一个分析测试问题和两个现实航空航天问题上演示了这一方法：一个问题的重点是高超音速摇摆机，采用不粘性气体动力学真实模型；另一个问题的重点是典型的ONERA M6机翼，采用粘性雷诺平均纳维-斯托克斯真实模型。在这两个例子中，梯度增强的深度GP都优于梯度增强的线性GP模型及其非梯度增强的对应模型。

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引用次数: 0

A fourth-order compact finite volume method on unstructured grids for simulation of two-dimensional incompressible flow 非结构网格上的四阶紧凑有限体积法模拟二维不可压缩流动

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2024-10-01 DOI: 10.1016/j.jcp.2024.113461

Ling Wen, Yan-Tao Yang, Qing-Dong Cai

This paper introduces a novel and efficient compact reconstruction procedure for high-order finite volume methods applied to unstructured grids. In this procedure, we establish a set of constitutive relations that ensure the continuity of the reconstruction polynomial and its normal derivatives between adjacent elements at control points. The paper delves into the details of the fourth-order compact reconstruction method specifically designed for two-dimensional triangular grids. This method can be considered an extension of the one-dimensional compact scheme and cubic spline interpolation methods to two-dimensional triangular unstructured grids. In the cubic polynomial reconstruction, a two-dimensional cubic polynomial is reconstructed using the cell averages of elements in the standard stencil and the function values at control points. The determination of function values at control points is achieved by adhering to the constraint of normal derivative continuity. This reconstruction is solved using a relaxation iteration method and has been verified to be solvable for triangular grids. Compared to other fourth-order implicit compact polynomial reconstructions, our method requires solving a smaller number of unknowns, which means less computational cost in reconstruction. By applying this method to solve the Poisson equation, the linear convection equation, and incompressible flow benchmarks, it demonstrates that the proposed method exhibits the expected high-order accuracy and performs well in incompressible flow problems.

本文为应用于非结构网格的高阶有限体积方法介绍了一种新颖、高效的紧凑重建程序。在该程序中，我们建立了一组构成关系，确保控制点上相邻元素之间重建多项式及其法导数的连续性。本文深入探讨了专为二维三角形网格设计的四阶紧凑重构方法的细节。该方法可视为一维紧凑方案和三次样条插值方法在二维三角形非结构网格上的扩展。在三次多项式重构中，利用标准模版中元素的单元平均值和控制点的函数值重构二维三次多项式。控制点上函数值的确定是通过遵守法线导数连续性约束来实现的。该重构采用松弛迭代法求解，并已验证可用于三角形网格。与其他四阶隐式紧凑多项式重构相比，我们的方法需要求解的未知数更少，这意味着重构的计算成本更低。通过应用这种方法求解泊松方程、线性对流方程和不可压缩流基准，证明了所提出的方法具有预期的高阶精度，在不可压缩流问题中表现良好。

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引用次数: 0