Search Results - Finite volume methods for initial value and initial-boundary value problems involving PDEs

Study of a New Low-Oscillating Second-Order All-Mach Number IMEX Finite Volume Scheme for the Full Euler Equations: Study of a new low-oscillating second-order all-Mach number IMEX finite volume scheme for the full Euler equations

Authors: Allegrini, P Vignal, Mh Vignal, Marie-Hélène

Contributors: Allegrini, P Vignal, Mh Vignal, Marie-Hélène

Source: SIAM Journal on Scientific Computing. 47:A268-A299

Subject Terms: high-order schemes, Asymptotic Preserving schemes, High-order schemes, [MATH] Mathematics [math], hyperbolic conservation laws, IMEX schemes, Error bounds for initial value and initial-boundary value problems involving PDEs, Finite volume methods for initial value and initial-boundary value problems involving PDEs, Hyperbolic conservation laws, Compressible fluids and gas dynamics, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, asymptotic preserving schemes, finite volumes, low Mach number limit, Low Mach number limit

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Semi-implicit Eulerian Method for the Fluid Structure Interaction of Elastic Membranes: Semi-implicit Eulerian method for the fluid structure interaction of elastic membranes

Authors: Ciallella, Mirco Milcent, Thomas

Source: SIAM Journal on Scientific Computing. 47:A1555-A1578

Subject Terms: Finite volume methods for initial value and initial-boundary value problems involving PDEs, Navier-Stokes equations for incompressible viscous fluids, Nonlinear elasticity, semi-implicit, FOS: Mathematics, fluid-structure interaction, immersed boundary, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Fictitious domain methods for initial value and initial-boundary value problems involving PDEs, incompressible Navier-Stokes, Eulerian elasticity

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Access URL: http://arxiv.org/abs/2310.19352
https://zbmath.org/8037168
https://doi.org/10.1137/23m1612512

The application of upwind meshless approximation finite volume method to the convection dominated problems on the unstructured and deformed meshes

Authors: C.K. Chou C.T. Wu L.H. Shen et al.

Source: Engineering Analysis with Boundary Elements. 155:717-737

Subject Terms: Finite volume methods for initial value and initial-boundary value problems involving PDEs, upwind scheme, deformed mesh, Navier-Stokes equations for incompressible viscous fluids, Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs, convection-diffusion equation, unstructured mesh, meshless method, finite volume method, Finite volume methods applied to problems in fluid mechanics

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Finite volume approximations of shear shallow water model on unstructured grids

Authors: Tiwari, Shashwat Nkonga, Boniface Chandrashekar, Praveen et al.

Contributors: Tiwari, Shashwat Nkonga, Boniface Chandrashekar, Praveen et al.

Source: The SMAI Journal of computational mathematics. 10:229-261

Subject Terms: [SDE] Environmental Sciences, Water waves, gravity waves, dispersion and scattering, nonlinear interaction, shear flow, [MATH] Mathematics [math], Finite volume methods applied to problems in fluid mechanics, PDEs in connection with fluid mechanics, non-conservative system, Shock waves and blast waves in fluid mechanics, 01 natural sciences, shallow flow, 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, 0103 physical sciences, 0101 mathematics

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Access URL: https://hal.science/hal-04403870v1/document
https://hal.science/hal-04403870v1
https://doi.org/10.5802/smai-jcm.112

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 et al.

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

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A Data-Driven Reconstruction for Unstructured Finite Volume Method on Multi-Dimensional Compressible Flows: A data-driven reconstruction for unstructured finite volume method on multi-dimensional compressible flows

Authors: Joo, Jayeon Kim, Dongseok You, Hojun et al.

Source: Communications in Computational Physics. 36:1307-1338

Subject Terms: machine learning, Finite volume methods for initial value and initial-boundary value problems involving PDEs, Learning and adaptive systems in artificial intelligence, tree model, shock-capturing method, Gas dynamics (general theory), Finite volume methods applied to problems in fluid mechanics, fully-connected neural network, Artificial neural networks and deep learning

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A space–time second-order algorithm based on finite volume method for Brinkman flow and reactive transport model in porous media with variable fractures: A space-time second-order algorithm based on finite volume method for Brinkman flow and reactive transport model in porous media with variable fractures

Authors: Wei Liu Pengshan Wang Gexian Fan

Source: Journal of Computational and Applied Mathematics. 462:116468

Subject Terms: Finite volume methods for initial value and initial-boundary value problems involving PDEs, Flows in porous media, filtration, seepage, Brinkman model, second-order algorithm, reactive transport, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Finite difference methods applied to problems in fluid mechanics, fractured porous media

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Access URL: https://zbmath.org/7988010
https://doi.org/10.1016/j.cam.2024.116468

Approximating Numerical Fluxes Using Fourier Neural Operators for Hyperbolic Conservation Laws: Approximating numerical fluxes using Fourier neural operators for hyperbolic conservation laws

Authors: Kim, Taeyoung Kang, Myungjoo

Source: Communications in Computational Physics. 37:420-456

Subject Terms: FOS: Computer and information sciences, Computer Science - Machine Learning, scientific machine learning, numerical analysis, Numerical Analysis (math.NA), PDE, neural operator, Machine Learning (cs.LG), Finite volume methods for initial value and initial-boundary value problems involving PDEs, Hyperbolic conservation laws, Finite difference methods for initial value and initial-boundary value problems involving PDEs, FOS: Mathematics, FNO, Mathematics - Numerical Analysis, conservation laws, Artificial neural networks and deep learning

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Access URL: http://arxiv.org/abs/2401.01783
https://zbmath.org/8033882
https://doi.org/10.4208/cicp.oa-2024-0123

Well-Balanced Fifth-Order Finite Volume WENO Schemes with Constant Subtraction Technique for Shallow Water Equations: Well-balanced fifth-order finite volume WENO schemes with constant subtraction technique for shallow water equations

Authors: Zhao, Lidan Tao, Zhanjing Zhang, Min

Source: Journal of Scientific Computing. 102

Subject Terms: Hydrology, hydrography, oceanography, Water waves, gravity waves, dispersion and scattering, nonlinear interaction, Geophysical flows, WENO, shallow water equations, Positive solutions to PDEs, Finite volume methods applied to problems in fluid mechanics, Numerical Analysis (math.NA), PDEs in connection with fluid mechanics, constant subtraction technique, Finite volume methods for initial value and initial-boundary value problems involving PDEs, FOS: Mathematics, Mathematics - Numerical Analysis, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, well-balanced

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Access URL: http://arxiv.org/abs/2411.11241

How to enforce an entropy inequality of (fully) well-balanced Godunov-type schemes for the shallow water equations

Authors: Martaud, Ludovic Berthon, Christophe

Source: ESAIM: Mathematical Modelling and Numerical Analysis. 59:955-997

Subject Terms: shallow water equations, Finite volume methods for initial value and initial-boundary value problems involving PDEs, well-balanced schemes, finite volume schemes, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, discrete entropy stability

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New adaptive low-dissipation central-upwind schemes

Authors: Shaoshuai Chu Alexander Kurganov Igor Menshov

Source: Applied Numerical Mathematics. 209:155-170

Subject Terms: Finite volume methods for initial value and initial-boundary value problems involving PDEs, Euler equations of gas dynamics, Hyperbolic conservation laws, low-dissipation central-upwind schemes, FOS: Mathematics, smoothness indicator, dissipative limiters, Finite volume methods applied to problems in fluid mechanics, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), Shock waves and blast waves in fluid mechanics, overcompressive limiters

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Access URL: http://arxiv.org/abs/2307.13356
https://zbmath.org/7984888
https://doi.org/10.1016/j.apnum.2024.11.010

Convergence of Lattice Boltzmann methods with overrelaxation for a nonlinear conservation law: Convergence of lattice Boltzmann methods with overrelaxation for a nonlinear conservation law

Authors: Denise Aregba-Driollet

Source: ESAIM: Mathematical Modelling and Numerical Analysis. 58:1935-1958

Subject Terms: Boltzmann equations, nonlinear conservation laws, convergence, Finite volume methods for initial value and initial-boundary value problems involving PDEs, lattice Boltzmann method, Hyperbolic conservation laws, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Kinetic theory of gases in time-dependent statistical mechanics, Particle methods and lattice-gas methods, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, First-order nonlinear hyperbolic equations

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A Semi-discrete Active Flux Method for the Euler Equations on Cartesian Grids: A semi-discrete active flux method for the Euler equations on Cartesian grids

Authors: Abgrall, Remi Barsukow, Wasilij Klingenberg, Christian et al.

Contributors: Abgrall, Remi Barsukow, Wasilij Klingenberg, Christian et al.

Source: Journal of Scientific Computing. 102

Subject Terms: Method of lines for initial value and initial-boundary value problems involving PDEs, Keywords Compressible Euler equations · Active flux · High, Finite volume methods for boundary value problems involving PDEs, Finite volume methods applied to problems in fluid mechanics, Numerical Analysis (math.NA), Euler equations, compressible Euler equations, 1712 Software, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, 10123 Institute of Mathematics, 510 Mathematics, 2604 Applied Mathematics, Finite volume methods for initial value and initial-boundary value problems involving PDEs, active flux, order methods Mathematics Subject Classification 65M08 · 65M20 · 65M70 · 76M12, high-order methods, 65M08, 65M20, 65M70, 76M12, 2200 General Engineering, Existence, uniqueness, and regularity theory for incompressible inviscid fluids, FOS: Mathematics, Mathematics - Numerical Analysis, 2614 Theoretical Computer Science, 2612 Numerical Analysis, 2605 Computational Mathematics, 1703 Computational Theory and Mathematics

File Description: application/xml; Abgrall2025_ASemiDiscreteActiveFluxMethod.pdf - application/pdf

Access URL: http://arxiv.org/abs/2310.00683
https://zbmath.org/7969181
https://doi.org/10.1007/s10915-024-02749-1

Error estimates in $ L^2 $ and $ L^\infty $ norms of finite volume method for the bilinear elliptic optimal control problem: Error estimates in \(L^2\) and \(L^\infty\) norms of finite volume method for the bilinear elliptic optimal control problem

Authors: Fei Cai Yin Yang Economics, Tianjin, China et al.

Source: AIMS Mathematics, Vol 6, Iss 8, Pp 8585-8599 (2021)

Subject Terms: a priori error estimates, Discrete approximations in optimal control, Finite volume methods for initial value and initial-boundary value problems involving PDEs, QA1-939, bilinear elliptic optimal control problem, variational discretization, finite volume method, PDE constrained optimization (numerical aspects), 0101 mathematics, 01 natural sciences, Mathematics

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Access URL: https://zbmath.org/7513709
https://doi.org/10.3934/math.2021498
https://doaj.org/article/c6a4fb205f8d4da28570318547f80745
https://www.aimspress.com/article/doi/10.3934/math.2021498

A Corrected $$H^T_N$$-UGKS for Boundary Layer Problems of the Gray Radiative Transfer Equations: A corrected \(H^T_N\)-UGKS for boundary layer problems of the gray radiative transfer equations

Authors: Song Jiang Qi Li Wenjun Sun

Source: Communications on Applied Mathematics and Computation. 7:689-717

Subject Terms: PDEs in connection with classical thermodynamics and heat transfer, Finite volume methods for initial value and initial-boundary value problems involving PDEs, implicit Monte Carlo (IMC) method, Research exposition (monographs, survey articles) pertaining to numerical analysis, boundary layer, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, nonlinear radiative transfer, \(H^T_N\)-UGKS, Asymptotic analysis for problems in thermodynamics and heat transfer

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Access URL: https://zbmath.org/8034295
https://doi.org/10.1007/s42967-024-00376-z

High-Order Well-Balanced Methods for the Euler Equations of Gas Dynamics with Gravitational Forces and the Ripa Model: High-order well-balanced methods for the Euler equations of gas dynamics with gravitational forces and the Ripa model

Authors: I. Gómez-Bueno M. J. Castro C. Parés

Source: RIUMA. Repositorio Institucional de la Universidad de Málaga
Universidad de Málaga

Subject Terms: Hydrology, hydrography, oceanography, finite volume methods, Método de los volúmenes finitos, Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations, reconstruction operators, Gas dynamics (general theory), Ecuaciones Euler, Compressible Euler equations, compressible Euler equations, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, High-order methods, Finite volume methods for initial value and initial-boundary value problems involving PDEs, Reconstruction operators, Finite-volume methods, Dinámica de gases, Finite volume methods for boundary value problems involving PDEs, Finite volume methods applied to problems in fluid mechanics, Euler equations, PDEs in connection with geophysics, high-order methods, Análisis matemático, well-balanced methods, Ripa model, Well-balanced methods, Análisis numérico

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Access URL: https://hdl.handle.net/10630/37656
https://zbmath.org/7983279
https://doi.org/10.1007/s10915-024-02781-1

Structure preserving hybrid Finite Volume Finite Element method for compressible MHD: Structure preserving hybrid finite volume finite element method for compressible MHD

Authors: Francesco Fambri Eric Sonnendrücker

Source: Journal of Computational Physics. 523:113691

Subject Terms: J.2, finite element exterior calculus (FEEC), G.1, semi-implicit, FOS: Physical sciences, Finite volume methods applied to problems in fluid mechanics, viscous resistive MHD, Numerical Analysis (math.NA), Physics - Plasma Physics, Plasma Physics (physics.plasm-ph), Finite volume methods for initial value and initial-boundary value problems involving PDEs, 65M60, 76M10, 85-08 (Primary) 65M12, 65M08, 76M12 (Secondary), structure preserving, all Mach, FOS: Mathematics, Magnetohydrodynamics and electrohydrodynamics, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Mathematics - Numerical Analysis, F.2.1, Astrophysics - Instrumentation and Methods for Astrophysics, finite volume, Instrumentation and Methods for Astrophysics (astro-ph.IM), Finite element methods applied to problems in fluid mechanics

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Access URL: http://arxiv.org/abs/2407.14141
https://zbmath.org/7986908
https://doi.org/10.1016/j.jcp.2024.113691

An Efficient Second-Order Finite Volume ADI Method for Nonlinear Three-Dimensional Space-Fractional Reaction-Diffusion Equations: An efficient second-order finite volume ADI method for nonlinear three-dimensional space-fractional reaction-diffusion equations

Authors: Zhang, Bingyin Fu, Hongfei Liang, Xueting et al.

Source: Advances in Applied Mathematics and Mechanics. 14:1400-1432

Subject Terms: Iterative numerical methods for linear systems, convergence, Finite volume methods for boundary value problems involving PDEs, finite volume method, Fractional partial differential equations, 01 natural sciences, Error bounds for initial value and initial-boundary value problems involving PDEs, efficient implementation, Finite volume methods for initial value and initial-boundary value problems involving PDEs, Fractional derivatives and integrals, Finite difference methods for initial value and initial-boundary value problems involving PDEs, nonlinear space-fractional reaction-diffusion equation, ADI, 0101 mathematics, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs

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Optimal control approach for moving bottom detection in one‐dimensional shallow waters by surface measurements: Optimal control approach for moving bottom detection in one-dimensional shallow waters by surface measurements

Authors: R. Lecaros J. López‐Ríos G. I. Montecinos et al.

Source: Mathematical Methods in the Applied Sciences. 47:13973-14004

Subject Terms: shallow water models, Water waves, gravity waves, dispersion and scattering, nonlinear interaction, bottom detection, Mathematics - Analysis of PDEs, Finite volume methods for initial value and initial-boundary value problems involving PDEs, finite volume methods, non-conservative hyperbolic systems, Existence, uniqueness, and regularity theory for incompressible inviscid fluids, Optimality conditions for problems involving partial differential equations, 49K20, 76B15, 76B03, 65M08, Mathematics - Numerical Analysis, Mathematics - Optimization and Control

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Access URL: http://arxiv.org/abs/2401.17239

Arbitrary-order unstructured finite-volume methods for implicit large eddy simulation of turbulent flows with adaptive dissipation/dispersion adjustment (ADDA)

Authors: Tsoutsanis, Panagiotis Nogueira, Xesus

Source: Journal of Computational Physics. 523:113653

Subject Terms: Finite volume methods for initial value and initial-boundary value problems involving PDEs, Direct numerical and large eddy simulation of turbulence, Finite volume methods applied to problems in fluid mechanics

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Access URL: https://zbmath.org/7986876
https://doi.org/10.1016/j.jcp.2024.113653