Validation Prediction of an Incompressible Flow in a Porous Medium–Free Stream System: Validation prediction of an incompressible flow in a porous medium-free stream system

Authors: Churbanov, A. G.

Source: Mathematical Models and Computer Simulations. 17:63-75

Subject Terms: Flows in porous media, filtration, seepage, Navier-Stokes equations for incompressible viscous fluids, finite element method, Darcy filtration model, averaged Navier-Stokes equations, Finite element methods applied to problems in fluid mechanics

File Description: application/xml

Efficient Fully Discrete Finite Element Scheme for the Ferrohydrodynamic Rosensweig Model and Simulations of Ferrofluid Rotational Flow Problems: Efficient fully discrete finite element scheme for the ferrohydrodynamic Rosensweig model and simulations of ferrofluid rotational flow problems

Authors: Guo-Dong Zhang, Xiaoming He, Xiaofeng Yang

Source: SIAM Journal on Scientific Computing. 47:B28-B58

Subject Terms: unconditional energy stability, decoupled, second-order, magnetic field, General theory of rotating fluids, PDEs in connection with fluid mechanics, Finite difference methods applied to problems in fluid mechanics, Suspensions, finite element, Magnetohydrodynamics and electrohydrodynamics, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Finite element methods applied to problems in fluid mechanics, ferrohydrodynamics

File Description: application/xml

Newton’s Method and its Hybrid with Machine Learning for Navier-Stokes Darcy Models Discretized by Mixed Element Methods: Newton's method and its hybrid with machine learning for Navier-Stokes Darcy models discretized by mixed element methods

Authors: Huang, Jianguo, Peng, Hui, Wu, Haohao

Source: Communications in Computational Physics. 37:30-60

Subject Terms: Error bounds for boundary value problems involving PDEs, Flows in porous media, filtration, seepage, FOS: Mathematics, deep learning, Navier Stokes-Darcy model, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Stability and convergence of numerical methods for boundary value problems involving PDEs, Int-Deep method, Finite element methods applied to problems in fluid mechanics, Newton iterative method, convergence analysis

File Description: application/xml

Access URL: http://arxiv.org/abs/2401.10557
https://zbmath.org/8013531
https://doi.org/10.4208/cicp.oa-2024-0066

The modelling error in multi-dimensional time-dependent solute transport models

Authors: Masri, Rami, Zeinhofer, Marius, Kuchta, Miroslav, Rognes, Marie E.

Source: arXiv

Subject Terms: Physiological flow, 0301 basic medicine, Smoothness and regularity of solutions to PDEs, Flows in porous media, filtration, seepage, Numerical Analysis (math.NA), PDEs in connection with fluid mechanics, Physiological flows, A priori estimates in context of PDEs, modeling error in evolving Bochner spaces, Diffusion, solute transport models, Second-order elliptic equations, 03 medical and health sciences, Error bounds for initial value and initial-boundary value problems involving PDEs, Mathematics - Analysis of PDEs, 0302 clinical medicine, 35K45, 65G99, 65J08, 65M15, 92-10, FOS: Mathematics, time dependent convection-diffusion, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, multi-dimensional modeling, Mathematics - Numerical Analysis, Computational methods for problems pertaining to biology, Finite element methods applied to problems in fluid mechanics, Analysis of PDEs (math.AP)

File Description: application/xml

Access URL: http://arxiv.org/abs/2303.17999
https://zbmath.org/7957223
https://doi.org/10.1051/m2an/2024060

$$L^2$$ norm convergence of IMEX BDF2 scheme with variable-step for the incompressible Navier-Stokes equations: \(L^2\) norm convergence of IMEX BDF2 scheme with variable-step for the incompressible Navier-Stokes equations

Authors: Ji, Bingquan, Zhao, Xuan

Source: Numerical Algorithms. 98:1917-1942

Subject Terms: incompressible Navier-Stokes equations, \(L^2\) norm error estimate, variable-step BDF2 method, discrete orthogonal convolution kernels, Navier-Stokes equations for incompressible viscous fluids, Finite element methods applied to problems in fluid mechanics

File Description: application/xml

Access URL: https://zbmath.org/8015102
https://doi.org/10.1007/s11075-024-01858-0

Natural convection analysis of magnetic nanofluid in fluid-magnetic coupled filed using the peridynamic differential operator

Authors: Zhanqi Cheng, Xihong Zhang, Yang Yang

Source: Engineering Analysis with Boundary Elements. 163:108-125

Subject Terms: fluid-magnetic coupled field, Peridynamics, Electromagnetic effects in solid mechanics, Non-Newtonian fluids, heat transfer, natural convection, magnetic nanofluid, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, peridynamic differential operator, Finite element methods applied to problems in fluid mechanics

File Description: application/xml

A comparison study of spatial and temporal schemes for flow and transport problems in fractured media with large parameter contrasts on small length scales

Authors: Wansheng Gao, Insa Neuweiler, Thomas Wick

Source: Computational Geosciences. 28:883-905

Subject Terms: space-time, finite differences, continuous Galerkin, fractured media, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, 0101 mathematics, 01 natural sciences, transport problems, Discontinuous Galerkin, Space-time, Original Paper, Continuous Galerkin, Fractured media, Finite differences, Transport problems, Finite element methods applied to problems in fluid mechanics, discontinuous Galerkin

File Description: application/xml

Access URL: https://zbmath.org/7966488
https://doi.org/10.1007/s10596-024-10293-y
https://repository.publisso.de/resource/frl:6500811

Error Estimates of Finite Element Method for the Incompressible Ferrohydrodynamics Equations: Error estimates of finite element method for the incompressible ferrohydrodynamics equations

Authors: Shipeng Mao, Jiaao Sun

Source: Communications on Applied Mathematics and Computation. 7:485-535

Subject Terms: Euler semi-implicit scheme, unconditional convergence, Error bounds for initial value and initial-boundary value problems involving PDEs, Maxwell equations, shliomis model, error estimates, mixed finite element methods, ferrofluids, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Stability and convergence of numerical methods for boundary value problems involving PDEs, PDEs in connection with fluid mechanics, Finite element methods applied to problems in fluid mechanics

File Description: application/xml

Access URL: https://zbmath.org/8034288
https://doi.org/10.1007/s42967-023-00347-w

Analysis and computation of a weak Galerkin scheme for solving the 2D/3D stationary Stokes interface problems with high-order elements

Authors: Kumar, Raman, Deka, Bhupen

Source: Journal of Numerical Mathematics. 32:347-367

Subject Terms: Error bounds for boundary value problems involving PDEs, Smoothness and regularity of solutions to PDEs, weak Galerkin methods, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Variational methods for elliptic systems, PDEs in connection with fluid mechanics, 01 natural sciences, Stokes and related (Oseen, etc.) flows, discontinuous viscosity, optimal error estimates, Second-order elliptic systems, 0101 mathematics, Stokes interface, Finite element methods applied to problems in fluid mechanics

File Description: application/xml

Quadrature-free forms of discontinuous Galerkin methods in solving compressible flows on triangular and tetrahedral grids

Authors: Wanai Li

Source: Mathematics and Computers in Simulation. 218:149-173

Subject Terms: quadrature free, nodal discontinuous Galerkin method, Hyperbolic conservation laws, unstructured grid, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, nonlinear stability, Finite element methods applied to problems in fluid mechanics, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs

File Description: application/xml

Access URL: https://zbmath.org/7833304
https://doi.org/10.1016/j.matcom.2023.11.030

Grad-Div Stabilized Finite Element Method for Magnetohydrodynamic Flows at Low Magnetic Reynolds Numbers: Grad-div stabilized finite element method for magnetohydrodynamic flows at low magnetic Reynolds numbers

Authors: Rong, Yao, Shi, Feng, Li, Yi, Zhang, Yuhong

Source: Journal of Mathematical Fluid Mechanics. 27

Subject Terms: backward Euler method, convergence, linear grad-div stabilization, well-posedness, Magnetohydrodynamics and electrohydrodynamics, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Finite element methods applied to problems in fluid mechanics

File Description: application/xml

Access URL: https://zbmath.org/8013100
https://doi.org/10.1007/s00021-025-00920-8

Semi-implicit Hybrid Finite Volume/Finite Element Method for the GPR Model of Continuum Mechanics: Semi-implicit hybrid finite volume/finite element method for the GPR model of continuum mechanics

Authors: Saray Busto, Laura Río-Martín

Contributors: Universidade de Santiago de Compostela. Departamento de Matemática Aplicada

Source: Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
Universidad de Santiago de Compostela (USC)

Subject Terms: Finite element methods, Continuum mechanics, numerical convergence analysis, smooth acoustic wave, fluid/solid circular explosion, spherical explosion, Gas dynamics (general theory), Finite volume methods applied to problems in fluid mechanics, structure-preserving scheme, Numerical Analysis (math.NA), Riemann problem, Finite volume methods, GPR model, FOS: Mathematics, Mathematics - Numerical Analysis, Semi-implicit structure-preserving scheme, Finite element methods applied to problems in fluid mechanics

File Description: application/pdf; application/xml

Access URL: http://arxiv.org/abs/2407.00823
https://hdl.handle.net/10347/40972
https://zbmath.org/7975322
https://doi.org/10.1007/s10915-024-02770-4
https://link.springer.com/article/10.1007/s10915-024-02770-4
https://hdl.handle.net/11572/444390
https://doi.org/10.1007/s10915-024-02770-4

Affine-Invariant WENO Operator on Nonuniform Cartesian Mesh with Application to Finite Volume and Discontinuous Galerkin Methods: Affine-invariant WENO operator on nonuniform Cartesian mesh with application to finite volume and discontinuous Galerkin methods

Authors: Xiang, Xiao-Shuo, Wang, Bao-Shan, Gao, Zhen, Li, Peng

Source: Journal of Scientific Computing. 102

Subject Terms: WENO, Finite volume methods for boundary value problems involving PDEs, Finite volume methods applied to problems in fluid mechanics, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Euler equations, Numerical quadrature and cubature formulas, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs, affine-invariant, finite volume scheme, Finite volume methods for initial value and initial-boundary value problems involving PDEs, DG method, Hyperbolic conservation laws, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, nonuniform mesh, Finite element methods applied to problems in fluid mechanics

File Description: application/xml

A Stokes–Dual–Porosity–Poroelasticity Model and Discontinuous Galerkin Method for the Coupled Free Flow and Dual Porosity Poroelastic Medium Problem: A Stokes-dual-porosity-poroelasticity model and discontinuous Galerkin method for the coupled free flow and dual porosity poroelastic medium problem

Authors: Rui Li, Chen-Song Zhang, Zhangxin Chen

Source: Journal of Scientific Computing. 102

Subject Terms: Flows in porous media, filtration, seepage, free flow, dual-porosity poroelasticity model, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, PDEs in connection with fluid mechanics, Stokes and related (Oseen, etc.) flows, Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.), Finite difference methods applied to problems in fluid mechanics, interface conditions, error estimates, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Soil and rock mechanics, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Finite element methods applied to problems in fluid mechanics, discontinuous Galerkin

File Description: application/xml

Access URL: https://zbmath.org/7969186
https://doi.org/10.1007/s10915-024-02771-3

Data Augmentation for the POD Formulation of the Parametric Laminar Incompressible Navier–Stokes Equations: Data augmentation for the formulation of the parametric laminar incompressible Navier-Stokes equations

Authors: Muixí Ballonga, Alba, Zlotnik, Sergio, Giacomini, Matteo, Díez, Pedro

Source: UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)

Subject Terms: Scientific machine learning, FOS: Computer and information sciences, Reduced-order models, Data augmentation, Incompressible Navier–Stokes, reduced-order model, Navier-Stokes equations for incompressible viscous fluids, Learning and adaptive systems in artificial intelligence, Fluid Dynamics (physics.flu-dyn), machine learning: jet flow control, FOS: Physical sciences, Physics - Fluid Dynamics, Numerical Analysis (math.NA), Proper orthogonal decomposition, Newton-Raphson method, Computational Engineering, Finance, and Science (cs.CE), proper orthogonal decomposition, lid-driven cavity, 65M60, 76D05, 76D55, FOS: Mathematics, Mathematics - Numerical Analysis, Computer Science - Computational Engineering, Finance, and Science, Finite element methods applied to problems in fluid mechanics

File Description: application/pdf; application/xml

Access URL: http://arxiv.org/abs/2312.14756
https://zbmath.org/7982176
https://doi.org/10.1002/nme.7624
https://hdl.handle.net/2117/425940
https://doi.org/10.1002/nme.7624

An Energy Stable Well‐Balanced Scheme for the Barotropic Euler System With Gravity Under the Anelastic Scaling: An energy stable well-balanced scheme for the barotropic Euler system with gravity under the anelastic scaling

Authors: K. R. Arun, Mainak Kar

Source: Numerical Methods for Partial Differential Equations. 41

Subject Terms: energy stability, Finite volume methods for boundary value problems involving PDEs, Asymptotic behavior of solutions to PDEs, MAC grid, Euler equations with gravity, finite volume method, Numerical Analysis (math.NA), Nonlinear elliptic equations, asymptotic preserving, Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics, Euler equations, Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs, A priori estimates in context of PDEs, Finite difference methods applied to problems in fluid mechanics, Integro-partial differential equations, Finite volume methods for initial value and initial-boundary value problems involving PDEs, Finite difference methods for initial value and initial-boundary value problems involving PDEs, anelastic limit, FOS: Mathematics, Primary 35L50, 35L60, 35L65, 35L67, Secondary 65M08, 65M12, Mathematics - Numerical Analysis, Weak solutions to PDEs, well-balanced, Finite element methods applied to problems in fluid mechanics

File Description: application/xml

Access URL: http://arxiv.org/abs/2405.00559

Structure Preserving Nodal Continuous Finite Elements via Global Flux Quadrature: Structure preserving nodal continuous finite elements via global flux quadrature

Authors: Wasilij Barsukow, Mario Ricchiuto, Davide Torlo

Contributors: Ricchiuto, Mario

Source: Numerical Methods for Partial Differential Equations. 41

Subject Terms: OSS, Hydro- and aero-acoustics, Numerical Analysis (math.NA), [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, PDE constrained optimization (numerical aspects), Euler equations, Numerical quadrature and cubature formulas, global flux quadrature, Finite difference methods applied to problems in fluid mechanics, stabilization, divergence preserving, finite elements, SUPG, very high-order, Numerical interpolation, Finite difference methods for initial value and initial-boundary value problems involving PDEs, FOS: Mathematics, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Mathematics - Numerical Analysis, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Finite element methods applied to problems in fluid mechanics

File Description: application/xml; application/pdf

Access URL: http://arxiv.org/abs/2407.10579
https://hal.science/hal-04779510v2/document
https://hal.science/hal-04779510v2

Fully decoupled, linear and unconditionally energy stable time discretization scheme for solving the unsteady thermally coupled magnetohydrodynamic equations with variable density

Authors: Yue Zhang, Xinlong Feng, Haiyan Su

Source: Applied Numerical Mathematics. 197:210-229

Subject Terms: incompressible Navier-Stokes equations, Maxwell equations, heat equation, Navier-Stokes equations for incompressible viscous fluids, conforming mixed finite element method, Magnetohydrodynamics and electrohydrodynamics, Diffusive and convective heat and mass transfer, heat flow, Finite element methods applied to problems in fluid mechanics

File Description: application/xml

A Locking-Free and Reduction-Free Conforming Finite Element Method for the Reissner-Mindlin Plate on Rectangular Meshes: A locking-free and reduction-free conforming finite element method for the Reissner-Mindlin plate on rectangular meshes

Authors: Zhang, Shangyou, Zhang, Zhimin

Source: Communications on Applied Mathematics and Computation. 7:470-484

Subject Terms: Reissner-Mindlin equation, Error bounds for boundary value problems involving PDEs, finite element, rectangular mesh, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, locking-free, Finite element methods applied to problems in fluid mechanics

File Description: application/xml

The moving finite element method with streamline-upwind Petrov–Galerkin for magnetohydrodynamic flows problems at high Hartmann numbers: The moving finite element method with streamline-upwind Petrov-Galerkin for magnetohydrodynamic flows problems at high Hartmann numbers

Authors: Xiaohua Zhang, Xinmeng Xu

Source: Engineering Analysis with Boundary Elements. 157:400-412

Subject Terms: high Hartmann numbers, streamline-upwind Petrov-Galerkin, Magnetohydrodynamics and electrohydrodynamics, moving mesh method, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, magnetohydrodynamic flows, Finite element methods applied to problems in fluid mechanics

File Description: application/xml