International Journal for Numerical Methods in Fluids最新文献

{"title":"Implicit coupling methods for nonlinear interactions between a large-deformable hyperelastic solid and a viscous acoustic fluid of infinite extent","authors":"Yapeng Li,&nbsp;Yegao Qu,&nbsp;Guang Meng","doi":"10.1002/fld.5242","DOIUrl":"10.1002/fld.5242","url":null,"abstract":"<p>This paper addresses the challenges in studying the interaction between high-intensity sound waves and large-deformable hyperelastic solids, which are characterized by nonlinearities of the hyperelastic material, the finite-amplitude acoustic wave, and the large-deformable fluid–solid interface. An implicit coupling method is proposed for predicting nonlinear structural-acoustic responses of the large-deformable hyperelastic solid submerged in a compressible viscous fluid of infinite extent. An arbitrary Lagrangian–Eulerian (ALE) formulation based on an unsplit complex-frequency-shifted perfectly matched layer method is developed for long-time simulation of the nonlinear acoustic wave propagation without exhibiting long-time instabilities. The solid and acoustic fluid domains are discretized using the finite element method, and two different options of staggered implicit coupling procedures for nonlinear structural-acoustic interactions are developed. Theoretical formulations for stability analysis of the implicit methods are provided. The accuracy, robustness, and convergence properties of the proposed methods are evaluated by a benchmark problem, that is, a hyperelastic rod interacting with finite-amplitude acoustic waves. The numerical results substantiate that the present methods are able to provide long-time steady-state solutions for a nonlinear coupled hyperelastic solid and viscous acoustic fluid system without numerical constraints of small time step sizes and long-time instabilities. The methods are applied to investigate nonlinear dynamic behaviors of coupled hyperelastic elliptical ring and acoustic fluid systems. Physical insights into 2:1 and 4:2:1 internal resonances of the hyperelastic elliptical ring and period-doubling bifurcations of the structural and acoustic responses of the system are provided.</p>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"96 3","pages":"231-255"},"PeriodicalIF":1.8,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135888673","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Coupling finite elements of class C1 on composite curved meshes for second order elliptic problems","authors":"Ashish Bhole,&nbsp;Hervé Guillard,&nbsp;Boniface Nkonga,&nbsp;Francesca Rapetti","doi":"10.1002/fld.5241","DOIUrl":"10.1002/fld.5241","url":null,"abstract":"<div>\u0000 \u0000 <p>Finite elements of class <math>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>𝒞</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow></math> are suitable for the computation of magnetohydrodynamics instabilities in tokamak plasmas. In addition, isoparametric approximations allow for a precise alignment of the mesh with the magnetic field line. Mesh alignment is crucial to achieve axisymmetric equilibria accurately. It is also helpful to deal with the anisotropy nature of magnetized plasma flows. In this numerical framework, several practical simulations are now available. They help to understand better the operation of existing devices and predict the optimal strategies for using the international ITER tokamak under construction. However, a mesh-aligned isoparametric representation suffers from the presence of critical points of the magnetic field (magnetic axis, X-point). We here explore a strategy that combines aligned mesh out of the critical points with non-aligned unstructured mesh in a region containing these points. By this strategy, we can avoid highly stretched elements and the numerical difficulties that come with them. The mesh-aligned interpolation uses bi-cubic Hemite-Bézier polynomials on a structured mesh of curved quadrangular elements. On the other hand, we assume reduced cubic Hsieh-Clough-Tocher finite elements on an unstructured triangular mesh. Both meshes overlap, and the resulting formulation is a coupled discrete problem solved iteratively by a suitable one-level Schwarz algorithm. In this paper, we will focus on the Poisson problem on a two-dimensional bounded regular domain. This elliptic equation is a simplified version of the axisymmetric tokamak equilibrium one at the asymptotic limit of infinite major radius (large aspect ratio).</p>\u0000 </div>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"96 2","pages":"209-230"},"PeriodicalIF":1.8,"publicationDate":"2023-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135197295","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Efficient hyperbolic–parabolic models on multi-dimensional unbounded domains using an extended DG approach","authors":"Federico Vismara,&nbsp;Tommaso Benacchio","doi":"10.1002/fld.5239","DOIUrl":"10.1002/fld.5239","url":null,"abstract":"<p>We introduce an extended discontinuous Galerkin discretization of hyperbolic–parabolic problems on multidimensional semi-infinite domains. Building on previous work on the one-dimensional case, we split the strip-shaped computational domain into a bounded region, discretized by means of discontinuous finite elements using Legendre basis functions, and an unbounded subdomain, where scaled Laguerre functions are used as a basis. Numerical fluxes at the interface allow for a seamless coupling of the two regions. The resulting coupling strategy is shown to produce accurate numerical solutions in tests on both linear and nonlinear scalar and vectorial model problems. In addition, an efficient absorbing layer can be simulated in the semi-infinite part of the domain in order to damp outgoing signals with negligible spurious reflections at the interface. By tuning the scaling parameter of the Laguerre basis functions, the extended DG scheme simulates transient dynamics over large spatial scales with a substantial reduction in computational cost at a given accuracy level compared to standard single-domain discontinuous finite element techniques.</p>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"96 2","pages":"161-188"},"PeriodicalIF":1.8,"publicationDate":"2023-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/fld.5239","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134958034","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An adaptive, training-free reduced-order model for convection-dominated problems based on hybrid snapshots","authors":"Victor Zucatti,&nbsp;Matthew J. Zahr","doi":"10.1002/fld.5240","DOIUrl":"10.1002/fld.5240","url":null,"abstract":"<p>The vast majority of reduced-order models (ROMs) first obtain a low dimensional representation of the problem from high-dimensional model (HDM) training data which is afterwards used to obtain a system of reduced complexity. Unfortunately, convection-dominated problems generally have a slowly decaying Kolmogorov <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 <annotation>$$ n $$</annotation>\u0000 </semantics></math>-width, which makes obtaining an accurate ROM built solely from training data very challenging. The accuracy of a ROM can be improved through enrichment with HDM solutions; however, due to the large computational expense of HDM evaluations for complex problems, they can only be used parsimoniously to obtain relevant computational savings. In this work, we exploit the local spatial coherence often exhibited by these problems to derive an accurate, cost-efficient approach that repeatedly combines HDM and ROM evaluations without a separate training phase. Our approach obtains solutions at a given time step by either fully solving the HDM or by combining partial HDM and ROM solves. A dynamic sampling procedure identifies regions that require the HDM solution for global accuracy and the reminder of the flow is reconstructed using the ROM. Moreover, solutions combining both HDM and ROM solves use spatial filtering to eliminate potential spurious oscillations that may develop. We test the proposed method on inviscid compressible flow problems and demonstrate speedups up to a factor of five.</p>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"96 2","pages":"189-208"},"PeriodicalIF":1.8,"publicationDate":"2023-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134958232","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Physics-based preconditioning of Jacobian-free Newton–Krylov solver for Navier–Stokes equations using nodal integral method","authors":"Nadeem Ahmed,&nbsp;Suneet Singh,&nbsp;Niteen Kumar","doi":"10.1002/fld.5236","DOIUrl":"10.1002/fld.5236","url":null,"abstract":"<p>The nodal integral methods (NIMs) have found widespread use in the nuclear industry for neutron transport problems due to their high accuracy. However, despite considerable development, these methods have limited acceptability among the fluid flow community. One major drawback of these methods is the lack of robust and efficient nonlinear solvers for the algebraic equations resulting from discretization. Since its inception, several modifications have been made to make NIMs more agile, efficient, and accurate. Modified nodal integral method (MNIM) and modified MNIM (M²NIM) are the two most recent and efficient versions of the NIM for fluid flow problems. M²NIM modifies the MNIM by replacing the current time convective velocity with the previous time convective velocity, leading to faster convergence albeit with reduced accuracy. This work proposes a preconditioned Jacobian-free Newton–Krylov approach for solving the Navier–Stokes equation using MNIM. The Krylov solvers do not generally work well without an appropriate preconditioner. Therefore, M²NIM is used here as a preconditioner to accelerate the solution of MNIM. Due to pressure–velocity coupling in the Navier–Stokes equation, developing a quality preconditioner for these equations needs significant effort. The momentum equation is solved using the time-splitting alternate direction implicit method. The velocities obtained from the solution are then used to solve the pressure Poisson equation. The computational results for the Navier–Stokes equation are presented to underscore the advantages of the developed algorithm.</p>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"96 2","pages":"138-160"},"PeriodicalIF":1.8,"publicationDate":"2023-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136309280","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Extension of moving particle simulation by introducing rotational degrees of freedom for dilute fiber suspensions","authors":"Keigo Enomoto,&nbsp;Takato Ishida,&nbsp;Yuya Doi,&nbsp;Takashi Uneyama,&nbsp;Yuichi Masubuchi","doi":"10.1002/fld.5235","DOIUrl":"10.1002/fld.5235","url":null,"abstract":"<p>We develop a novel Moving Particle Simulation (MPS) method to reproduce the motion of fibers floating in sheared liquids accurately. In conventional MPS schemes, if a fiber suspended in a liquid is represented by a one-dimensional array of MPS particles, it is entirely aligned to the flow direction due to the lack of shear stress difference between fiber–liquid interfaces. To address this problem, we employ the micropolar fluid model to introduce rotational degrees of freedom into the MPS particles. The translational motion of liquid and solid particles and the rotation of solid particles are calculated with the explicit MPS algorithm. The fiber is modeled as an array of micropolar fluid particles bonded with stretching, bending and torsional potentials. The motion of a single rigid fiber is simulated in a three-dimensional shear flow generated between two moving solid walls. We show that the proposed method is capable of reproducing the fiber motion predicted by Jeffery's theory which is different from the conventional MPS simulations.</p>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"96 2","pages":"125-137"},"PeriodicalIF":1.8,"publicationDate":"2023-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136306902","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Accelerated solutions of convection-dominated partial differential equations using implicit feature tracking and empirical quadrature","authors":"Marzieh Alireza Mirhoseini,&nbsp;Matthew J. Zahr","doi":"10.1002/fld.5234","DOIUrl":"10.1002/fld.5234","url":null,"abstract":"<div>\u0000 \u0000 <p>This work introduces an empirical quadrature-based hyperreduction procedure and greedy training algorithm to effectively reduce the computational cost of solving convection-dominated problems with limited training. The proposed approach circumvents the slowly decaying <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 <annotation>$$ n $$</annotation>\u0000 </semantics></math>-width limitation of linear model reduction techniques applied to convection-dominated problems by using a nonlinear approximation manifold systematically defined by composing a low-dimensional affine space with bijections of the underlying domain. The reduced-order model is defined as the solution of a residual minimization problem over the nonlinear manifold. An online-efficient method is obtained by using empirical quadrature to approximate the optimality system such that it can be solved with mesh-independent operations. The proposed reduced-order model is trained using a greedy procedure to systematically sample the parameter domain. The effectiveness of the proposed approach is demonstrated on two shock-dominated computational fluid dynamics benchmarks.</p>\u0000 </div>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"96 1","pages":"102-124"},"PeriodicalIF":1.8,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135436100","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"WENO smoothness indicator based troubled-cell indicator for hyperbolic conservation laws","authors":"K. R. Arun,&nbsp;Asha K. Dond,&nbsp;Rakesh Kumar","doi":"10.1002/fld.5237","DOIUrl":"10.1002/fld.5237","url":null,"abstract":"<div>\u0000 \u0000 <p>Hybrid algorithms are an efficient and popular choice for computing the solutions of hyperbolic conservation laws. In general, hybrid algorithms involve low-cost high-order accurate schemes in smooth regions and non-oscillatory shock-capturing schemes in the vicinity of discontinuities. Troubled-cell indicators which measure the smoothness of the solution play a significant role in the efficiency of hybrid algorithms. This article proposes a new troubled-cell indicator utilising the smoothness indicators of WENO schemes for hyperbolic conservation laws. The proposed troubled-cell indicators are simple, efficient, effective, and are used to construct three new adaptive WENO algorithms of high-order accuracy. The hybrid algorithms developed are independent of the order and type of the WENO reconstruction. For demonstration, we have considered the fifth and seventh order WENO-Z reconstruction. The first two algorithms have comparable accuracy and resolution of the solution across discontinuities to that of the WENO-Z scheme but at a less computational cost. The third algorithm ensures the convergence of the proposed scheme to the correct entropy solution when applied to a hyperbolic conservation law with non-convex flux for which the WENO schemes fail. We have performed several 1D and 2D numerical experiments to demonstrate the efficiency of the proposed algorithms and their performance compared with the WENO-Z schemes. The proposed algorithms are efficient and take 30%–75% less computational time than the WENO-Z schemes while retaining the advantages of WENO-Z schemes.</p>\u0000 </div>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"96 1","pages":"44-86"},"PeriodicalIF":1.8,"publicationDate":"2023-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134912215","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Deep learning-based method for solving seepage equation under unsteady boundary","authors":"Daolun Li,&nbsp;Luhang Shen,&nbsp;Wenshu Zha,&nbsp;Shuaijun Lv","doi":"10.1002/fld.5238","DOIUrl":"10.1002/fld.5238","url":null,"abstract":"<p>Deep learning-based methods for solving partial differential equations have become a research hotspot. The approach builds on the previous work of applying deep learning methods to partial differential equations, which avoid the need for meshing and linearization. However, deep learning-based methods face difficulties in effectively solving complex turbulent systems without using labeled data. Moreover, issues such as failure to converge and unstable solution are frequently encountered. In light of this objective, this paper presents an approximation-correction model designed for solving the seepage equation featuring unsteady boundaries. The model consists of two neural networks. The first network acts as an asymptotic block, estimating the progression of the solution based on its asymptotic form. The second network serves to fine-tune any errors identified in the asymptotic block. The solution to the unsteady boundary problem is achieved by superimposing these progressive blocks. In numerical experiments, both a constant flow scenario and a three-stage flow scenario in reservoir exploitation are considered. The obtained results show the method's effectiveness when compared to numerical solutions. Furthermore, the error analysis reveals that this method exhibits superior solution accuracy compared to other baseline methods.</p>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"96 1","pages":"87-101"},"PeriodicalIF":1.8,"publicationDate":"2023-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134911769","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Variable passing method for combining 3D MPM–FEM hybrid and 2D shallow water simulations of landslide-induced tsunamis","authors":"Shaoyuan Pan,&nbsp;Reika Nomura,&nbsp;Guoming Ling,&nbsp;Shinsuke Takase,&nbsp;Shuji Moriguchi,&nbsp;Kenjiro Terada","doi":"10.1002/fld.5233","DOIUrl":"10.1002/fld.5233","url":null,"abstract":"<p>With a view to simulating the entire process of a landslide-triggered tsunami, ranging from tsunami generation to offshore wave propagation, with relatively low computational costs, we present a 2D–3D coupling strategy to bridge 3D MPM–FEM hybrid and 2D shallow water (SW) simulations. Specifically, considering the difference in basis functions between the 3D and 2D analysis methods, we devise a novel variable passing scheme in the domain overlapping method, in which a slightly overlapped domain enables the generated wave to pass through the connection boundaries with as little discrepancy as possible. For the tsunami generation stage in the 3D domain, the hybrid method combining the finite element method (FEM) and material point method (MPM) is adopted. In this method, the 3D governing equation of the solid phase is solved with the MPM, whereas the well-established 3D stabilized FEM is applied to that of the fluid phase in an Eulerian frame. Additionally, the phase-field method is employed to track the free surface of the 3D fluid domain. On the other hand, the SW equation that represents the offshore wave motion in the 2D domain is solved by the 2D stabilized FEM. Several numerical examples are presented to demonstrate the effectiveness of the developed scheme in properly passing the data from 3D/2D to 2D/3D domains.</p>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"96 1","pages":"17-43"},"PeriodicalIF":1.8,"publicationDate":"2023-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44931729","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}