Journal of Computational Physics最新文献

{"title":"Jump penalty stabilization techniques for under-resolved turbulence in discontinuous Galerkin schemes","authors":"Jiaqing Kou ,&nbsp;Oscar A. Marino ,&nbsp;Esteban Ferrer","doi":"10.1016/j.jcp.2023.112399","DOIUrl":"10.1016/j.jcp.2023.112399","url":null,"abstract":"<div><p>Jump penalty stabilization techniques for under-resolved turbulence have been recently proposed for continuous and discontinuous high order Galerkin schemes <span>[1]</span>, <span>[2]</span>, <span>[3]</span>. The stabilization relies on the gradient or solution discontinuity at element interfaces to incorporate localised numerical diffusion in the numerical scheme. This diffusion acts as an implicit subgrid model and stabilizes under-resolved turbulent simulations.</p><p>This paper investigates the effect of jump penalty stabilization methods (penalising gradient or solution) for stabilization and improvement of high-order discontinuous Galerkin schemes in turbulent regime. We analyze these schemes using an eigensolution analysis, a 1D non-linear Burgers equation (mimicking a turbulent cascade) and 3D turbulent Navier-Stokes simulations (Taylor-Green Vortex and Kelvin-Helmholtz Instability problems).</p><p>We show that the two jump penalty stabilization techniques can stabilize under-resolved simulations thanks to the improved dispersion-dissipation characteristics (when compared to non-penalized schemes) and provide accurate results for turbulent flows. The numerical results indicate that the proposed jump penalty methods stabilize under-resolved simulations and improve the simulations, when compared to the original unpenalized scheme and to classic explicit subgrid models (Smagorinsky and Vreman).</p></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"491 ","pages":"Article 112399"},"PeriodicalIF":4.1,"publicationDate":"2023-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0021999123004941/pdfft?md5=dbbdd7556718ce6c831a5d3f5df1aa48&pid=1-s2.0-S0021999123004941-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74832780","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Influences of conservative and non-conservative Lorentz forces on energy conservation properties for incompressible magnetohydrodynamic flows","authors":"Hideki Yanaoka","doi":"10.1016/j.jcp.2023.112372","DOIUrl":"10.1016/j.jcp.2023.112372","url":null,"abstract":"<div><p><span><span>In the analysis of magnetohydrodynamic (MHD) flow, the Lorentz force<span><span> significantly affects energy properties because the work generated by the Lorentz force changes the kinetic and magnetic energies. Therefore, the Lorentz force and energy conversion should be predicted accurately. Some energy conservation schemes have been proposed and validated. However, the influences of the Lorentz force discretization on conservation and conversion of energy have not yet been clarified. In this study, a conservative </span>finite difference method<span> is constructed for incompressible MHD flows considering the induced magnetic field. We compare the difference in energy conservation properties among three methods of calculating the Lorentz force. The Lorentz forces are calculated in conservative and non-conservative forms, and both compact and wide-range interpolations of magnetic flux density are used to calculate the non-conservative Lorentz force. The compact interpolation method proposed in this study can perform conversions between conservative and non-conservative forms of the Lorentz force even when using the finite difference method. The present </span></span></span>numerical method improves the conservation of transport quantity. Five models were analyzed, and the accuracy and convergence of the present numerical method were verified. From the viewpoint of the conservation of the total energy in an ideal inviscid periodic MHD flow, we consider that the calculation using compact interpolation for the Lorentz force is appropriate. This method preserves the total energy even on non-uniform grids. Moreover, the divergence-free condition of the magnetic flux density is discretely satisfied even without the correction of the magnetic flux density. The present numerical method can capture the Hartmann layer in the propagation of an </span>Alfvén wave<span><span> and accurately predict the tendency of energy attenuation in the analysis of a Taylor decaying vortex under magnetic fields. Analysis of the Orszag–Tang vortex reveals </span>energy dissipation processes and the generation of high current densities. The present numerical method has excellent energy conservation properties and can accurately predict energy conversion. Therefore, this method can contribute to understanding complex unsteady MHD flows.</span></p></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"491 ","pages":"Article 112372"},"PeriodicalIF":4.1,"publicationDate":"2023-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79290935","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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}

{"title":"Multi-dimensional summation-by-parts operators for general function spaces: Theory and construction","authors":"Jan Glaubitz ,&nbsp;Simon-Christian Klein ,&nbsp;Jan Nordström ,&nbsp;Philipp Öffner","doi":"10.1016/j.jcp.2023.112370","DOIUrl":"10.1016/j.jcp.2023.112370","url":null,"abstract":"<div><p>Summation-by-parts (SBP) operators allow us to systematically develop energy-stable and high-order accurate numerical methods for time-dependent differential equations. Until recently, the main idea behind existing SBP operators was that polynomials can accurately approximate the solution, and SBP operators should thus be exact for them. However, polynomials do not provide the best approximation for some problems, with other approximation spaces being more appropriate. We recently addressed this issue and developed a theory for <em>one-dimensional</em> SBP operators based on general function spaces, coined function-space SBP (FSBP) operators. In this paper, we extend the theory of FSBP operators to <em>multiple dimensions</em>. We focus on their existence, connection to quadratures, construction, and mimetic properties. A more exhaustive numerical demonstration of multi-dimensional FSBP (MFSBP) operators and their application will be provided in future works. Similar to the one-dimensional case, we demonstrate that most of the established results for polynomial-based multi-dimensional SBP (MSBP) operators carry over to the more general class of MFSBP operators. Our findings imply that the concept of SBP operators can be applied to a significantly larger class of methods than is currently done. This can increase the accuracy of the numerical solutions and/or provide stability to the methods.</p></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"491 ","pages":"Article 112370"},"PeriodicalIF":4.1,"publicationDate":"2023-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0021999123004655/pdfft?md5=1cd58bc50f14ad8b9c9814729f56d930&pid=1-s2.0-S0021999123004655-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81936749","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"DeepStSNet: Reconstructing the quantum state-resolved thermochemical nonequilibrium flowfield using deep neural operator learning with scarce data","authors":"Jiaqi Lv ,&nbsp;Qizhen Hong ,&nbsp;Xiaoyong Wang ,&nbsp;Zhiping Mao ,&nbsp;Quanhua Sun","doi":"10.1016/j.jcp.2023.112344","DOIUrl":"10.1016/j.jcp.2023.112344","url":null,"abstract":"&lt;div&gt;&lt;p&gt;&lt;span&gt;The hypersonic flow&lt;span&gt;&lt;span&gt; is in a thermochemical nonequilibrium state due to the high-temperature caused by the strong shock compression. In a thermochemical nonequilibrium flow&lt;span&gt;, the distribution of molecular internal energy levels strongly deviates from the equilibrium distribution (i.e., the Boltzmann distribution). It is intractable to directly obtain the microscopic nonequilibrium distribution from existed experimental measurements usually described by macroscopic field variables such as temperature or velocity. Motivated by the idea of deep multi-scale multi-physics &lt;/span&gt;&lt;/span&gt;neural network (DeepMMNet) proposed in &lt;/span&gt;&lt;/span&gt;&lt;span&gt;[1]&lt;/span&gt;&lt;span&gt;, we develop in this paper a data assimilation framework called &lt;/span&gt;&lt;em&gt;DeepStSNet&lt;/em&gt; to accurately reconstruct the quantum state-resolved thermochemical nonequilibrium flowfield by using &lt;em&gt;sparse experimental measurements&lt;/em&gt;&lt;span&gt;&lt;span&gt;&lt;span&gt; of vibrational temperature and pre-trained deep neural operator networks (DeepONets). In particular, we first construct several DeepONets to express the coupled dynamics between field variables in the thermochemical nonequilibrium flow and to approximate the state-to-state (StS) approach, which traces the variation of each vibrational level of molecule accurately. These proposed DeepONets are then trained by using the numerical simulation data, and would later be served as building blocks for the DeepStSNet. We demonstrate the effectiveness and accuracy of DeepONets with different test cases showing that the density and energy of vibrational groups as well as the temperature and velocity fields are predicted with high accuracy. We then extend the architectures of DeepMMNet by considering a simplified thermochemical nonequilibrium model, i.e., the 2T model, showing that the entire thermochemical nonequilibrium flowfield is well predicted by using scattered measurements of full or even partial field variables. We next consider a more accurate and complex thermochemical nonequilibrium model, i.e., the StS-CGM model, and develop a DeepStSNet for this model. In this case, we employ the coarse-grained method, which divides the vibrational levels into groups (vibrational bins), to alleviate the computational cost for the StS approach in order to achieve a fast but reliable prediction with DeepStSNet. We test the present DeepStSNet framework with sparse numerical simulation data showing that the predictions are in excellent agreement with the reference data for test cases. We further employ the DeepStSNet to assimilate a few experimental measurements of vibrational temperature obtained from the &lt;/span&gt;shock tube experiment, and the detailed non-Boltzmann vibrational distribution of molecule oxygen is reconstructed by using the sparse experimental data for the first time. Moreover, by considering the inevitable uncertainty in the experimental data, an average strategy in the predicting procedure is proposed to obtain the most p","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"491 ","pages":"Article 112344"},"PeriodicalIF":4.1,"publicationDate":"2023-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74814049","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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}

{"title":"An extended model for the direct numerical simulation of droplet evaporation. Influence of the Marangoni convection on Leidenfrost droplet","authors":"Guillaume Mialhe,&nbsp;Sébastien Tanguy,&nbsp;Léo Tranier,&nbsp;Elena-Roxana Popescu,&nbsp;Dominique Legendre","doi":"10.1016/j.jcp.2023.112366","DOIUrl":"10.1016/j.jcp.2023.112366","url":null,"abstract":"<div><p><span>In this paper, we propose an extended model for the numerical simulation of evaporating droplets within the framework of interface capturing or interface tracking methods. Most existing works make several limiting assumptions that need to be overcome for a more accurate description of the evaporation of droplets. In particular, the variations of several physical variables with local temperature and mass fraction fields must be accounted for in order to perform more realistic computations. While taking into account the variations of some of these physical properties, as viscosity, seems rather obvious, variations of other variables, as density and surface tension, involve additional source terms in the fundamental equations for which a suitable discretization must be developed. The paper presents a numerical strategy to account for such an extended model along with several original test-cases allowing to demonstrate both the accuracy of the proposed numerical schemes and the strong interest in developing such an extended model for the simulation of droplet evaporation. In particular, the impact of thermo-capillary convection will be highlighted on the vapor film thickness between a superheated wall and a </span>static Leidenfrost droplet levitating above this wall.</p></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"491 ","pages":"Article 112366"},"PeriodicalIF":4.1,"publicationDate":"2023-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75494078","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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}

{"title":"A non-intrusive data-driven reduced order model for parametrized CFD-DEM numerical simulations","authors":"Arash Hajisharifi ,&nbsp;Francesco Romanò ,&nbsp;Michele Girfoglio ,&nbsp;Andrea Beccari ,&nbsp;Domenico Bonanni ,&nbsp;Gianluigi Rozza","doi":"10.1016/j.jcp.2023.112355","DOIUrl":"10.1016/j.jcp.2023.112355","url":null,"abstract":"<div><p>The investigation of fluid-solid systems is very important in a lot of industrial processes. From a computational point of view, the simulation of such systems is very expensive, especially when a huge number of parametric configurations needs to be studied. In this context, we develop a non-intrusive data-driven reduced order model (ROM) built using the proper orthogonal decomposition<span><span> with interpolation (PODI) method for Computational Fluid Dynamics (CFD) - Discrete Element Method (DEM) simulations. The main novelties of the proposed approach rely in (i) the combination of ROM and </span>FV methods, (ii) a numerical sensitivity analysis of the ROM accuracy with respect to the number of POD modes and to the cardinality of the training set and (iii) a parametric study with respect to the Stokes number. We test our ROM on the fluidized bed benchmark problem. The accuracy of the ROM is assessed against results obtained with the FOM both for Eulerian (the fluid volume fraction) and Lagrangian (position and velocity of the particles) quantities. We also discuss the efficiency of our ROM approach.</span></p></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"491 ","pages":"Article 112355"},"PeriodicalIF":4.1,"publicationDate":"2023-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82634014","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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}

{"title":"Spectral deferred correction method for Landau–Brazovskii model with convex splitting technique","authors":"Donghang Zhang ,&nbsp;Lei Zhang","doi":"10.1016/j.jcp.2023.112348","DOIUrl":"10.1016/j.jcp.2023.112348","url":null,"abstract":"<div><p>The Landau–Brazovskii model is a well-known Landau model for finding the complex phase structures in microphase-separating systems ranging from block copolymers<span> to liquid crystals. It is critical to design efficient numerical schemes for the Landau–Brazovskii model with energy dissipation<span><span> and mass conservation properties. Here, we propose a mass conservative and energy stable scheme by combining the spectral deferred correction (SDC) method with the convex splitting technique to solve the Landau–Brazovskii model efficiently. An adaptive correction strategy for the SDC method is implemented to reduce the cost time and preserve energy stability. Numerical experiments, including two- and three-dimensional periodic crystals in Landau–Brazovskii model, are presented to show the efficiency of the proposed </span>numerical method.</span></span></p></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"491 ","pages":"Article 112348"},"PeriodicalIF":4.1,"publicationDate":"2023-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76617346","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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}

{"title":"Tensor rank reduction via coordinate flows","authors":"Alec Dektor,&nbsp;Daniele Venturi","doi":"10.1016/j.jcp.2023.112378","DOIUrl":"10.1016/j.jcp.2023.112378","url":null,"abstract":"<div><p>Recently, there has been a growing interest in efficient numerical algorithms based on tensor networks and low-rank techniques to approximate high-dimensional functions and solutions to high-dimensional PDEs. In this paper, we propose a new tensor rank reduction method based on coordinate transformations that can greatly increase the efficiency of high-dimensional tensor approximation algorithms. The idea is simple: given a multivariate function, determine a coordinate transformation so that the function in the new coordinate system has smaller tensor rank. We restrict our analysis to linear coordinate transformations, which gives rise to a new class of functions that we refer to as tensor ridge functions. Leveraging Riemannian gradient descent on matrix manifolds we develop an algorithm that determines a quasi-optimal linear coordinate transformation for tensor rank reduction. The results we present for rank reduction via linear coordinate transformations open the possibility for generalizations to larger classes of nonlinear transformations.</p></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"491 ","pages":"Article 112378"},"PeriodicalIF":4.1,"publicationDate":"2023-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0021999123004734/pdfft?md5=f13c9934371c08d511cc5f5b8ba637fb&pid=1-s2.0-S0021999123004734-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81535384","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A mass transfer cavitation model for the numerical flow simulation of binary alkane mixture segregation","authors":"Philip Schwarz,&nbsp;Romuald Skoda","doi":"10.1016/j.jcp.2023.112382","DOIUrl":"10.1016/j.jcp.2023.112382","url":null,"abstract":"<div><p><span><span>Based on the Rayleigh bubble dynamics equation a mass transfer model for cavitation of binary alkane mixtures is presented. Raoult's and </span>Dalton's law<span>, simple mixing rules, and an accurate Equation of State<span> are utilized. The model is implemented into an in-house CFD code. For solver validation pure species literature cases are taken. The method is applied to a lighter </span></span></span><em>n</em>-octane/<em>n</em>-heptane and a heavier <em>n</em>-dodecane/<em>n</em><span><span>-heptane mixture in a rarefaction tube and a </span>hydrofoil test case. Segregation of the species is observed during cavitation due to their different mass transfer rates. While for the lighter mixture, mass transfer of both species only moderately deviates, a significantly higher mass transfer of </span><em>n</em>-heptane compared to <em>n</em>-dodecane is observed for the heavier mixture, where the saturation pressure differs two orders of magnitude between the mixture ingredients. The strong segregation of the heavier mixture is associated with a predominant amount of <em>n</em>-heptane in the vapor phase. As a consequence, vapor composition is strongly affected by the volatilities of mixture ingredients.</p></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"491 ","pages":"Article 112382"},"PeriodicalIF":4.1,"publicationDate":"2023-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83950546","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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}

{"title":"Efficient energy structure-preserving schemes for three-dimensional Maxwell's equations","authors":"Linghua Kong ,&nbsp;Peng Zhang ,&nbsp;Meng Chen","doi":"10.1016/j.jcp.2023.112357","DOIUrl":"https://doi.org/10.1016/j.jcp.2023.112357","url":null,"abstract":"<div><p><span>Two energy structure-preserving schemes are proposed for Maxwell's equations in three dimensions. The Maxwell's equations are split into several local one-dimensional subproblems which successfully reduces the scale of </span>algebraic equations<span> to be solved. To improve the convergence rate in space and to keep the sparsity of the resulting algebraic equations, the spatial derivatives are approximated by high order compact method. Some key indicators, such as stability, energy structure-preserving and convergence of the schemes are investigated. To make the theoretical more persuasive, some numerical examples are shown. Numerical results are accord with the theoretical results. This provides a practical approach to construct efficient structure-preserving algorithms multidimensional Maxwell's equations.</span></p></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"491 ","pages":"Article 112357"},"PeriodicalIF":4.1,"publicationDate":"2023-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72248383","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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}