Online citations, reference lists, and bibliographies.
← Back to Search

A Fast High-resolution Algorithm For Linear Convection Problems: Particle Transport Method

A. Smolianski, O. Shipilova, H. Haario
Published 2007 · Mathematics

Save to my Library
Download PDF
Analyze on Scholarcy Visualize in Litmaps
Share
Reduce the time it takes to create your bibliography by a factor of 10 by using the world’s favourite reference manager
Time to take this seriously.
Get Citationsy
The paper is devoted to a novel explicit technique, the particle transport method (PTM), for solving linear convection problems. While being a Lagrangian (characteristic based) method, PTM has the advantage of Eulerian methods to represent the solution on a fixed mesh. The proposed approach belongs to the class of monotone high-resolution numerical schemes, possesses the property of unconditional stability and works with structured and unstructured meshes. It is also demonstrated that the method has a linear computational complexity. The performance of the presented algorithm is tested on one- and two-dimensional benchmark problems. The numerical results confirm that the method has the 2nd-order spatial accuracy and can be significantly faster than the grid-based methods of the same order. Copyright © 2006 John Wiley & Sons, Ltd.
This paper references
10.1007/3-540-05407-3_6
Flag: A free-Lagrange method for numerically simulating hydrodynamic flows in two dimensions
W. P. Crowley (1971)
Stream-line Upwind/Petrov-Galerkin formulation for convection dominated flows with particular emphasis on the incompressible Navier- Stokes equations
Brooks A N Hughes (1982)
Stream - line Upwind / Petrov - Galerkin formulation for convection dominated flows with particular emphasis on the incompressible Navier - Stokes equations
N. BrooksA. (1982)
10.1002/NME.1620200108
A Taylor–Galerkin method for convective transport problems
J. Donea (1983)
10.1016/0045-7825(86)90152-0
A new finite element formulation for computational fluid dynamics: III. The generalized streamline operator for multidimensional advective-diffusive systems
T. Hughes (1986)
10.1016/0045-7825(87)90125-3
A new finite element formulation for computational fluid dynamics: VI. Convergence analysis of the generalized SUPG formulation for linear time-dependent multi-dimensional advective-diffusive systems
T. J. Hughes (1987)
10.1002/FLD.1650071007
Finite Element Flux-Corrected Transport (FEM-FCT) for the Euler and Navier-Stokes equations
R. Löhner (1987)
10.1016/0021-9991(87)90031-3
Uniformly high order accurate essentially non-oscillatory schemes, 111
A. Harten (1987)
Uniformly high order essentially non-oscillatory schemes, III
A. Harten (1987)
Uniformly high order essentially non-oscillatory schemes
A Harten (1987)
10.1051/M2AN/1988220406251
Stability of the Lagrange-Galerkin method with non-exact integration
K. Morton (1988)
10.1016/0021-9991(89)90222-2
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
C. Shu (1989)
10.1016/S1570-8659(05)80035-3
Splitting and alternating direction methods
G. Marchuk (1990)
10.1016/0045-7825(82)90071-8
Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
A. Brooks (1990)
Splitting and alternating direction methods In Handbook of Numerical Analysis I, Noth-Holland
G I Marchuk (1990)
10.1016/0045-7825(92)90139-B
An introduction to finite element methods for transient advection problems
J. Donea (1992)
10.1142/9789814354561_0013
High resolution schemes for hyperbolic conservation laws
C. Angelopoulos (1992)
10.1016/0045-7825(92)90114-Y
A new approach to algorithms for convection problems which are based on exact transport + projection
Claes Johnson (1992)
Numerical methods for problems with moving fronts
B. Finlayson (1992)
10.1007/978-3-0348-8629-1_3
Scalar Conservation Laws
R. LeVeque (1992)
10.1016/0045-7825(93)90189-5
Petrov-Galerkin solutions of the incompressible Navier-Stokes equations in primitive variables with adaptive remeshing
P. A. B. D. Sampaio (1993)
10.1007/BF00370489
Eulerian-Lagrangian localized adjoint methods for linear advection or advection-reaction equations and their convergence analysis
R. Ewing (1993)
10.1006/JCPH.1993.1091
A Finite-Volume High-Order ENO Scheme for Two-Dimensional Hyperbolic Systems
J. Casper (1993)
10.1006/JCPH.1994.1104
Exact projections and the Lagrange-Galerkin method: a realistic alternative to quadrature
A. Priestley (1994)
10.1006/JCPH.1994.1034
Simulating Free Surface Flows with SPH
J. Monaghan (1994)
10.1002/FLD.1650200805
Positive schemes and shock modelling for compressible flows
A. Jameson (1995)
10.1006/JCPH.1995.1107
Robust, Vectorized Search Algorithms for Interpolation on Unstructured Grids
R. Löhner (1995)
10.1016/S0045-7825(96)01078-X
Meshless methods: An overview and recent developments
T. Belytschko (1996)
10.1006/JCPH.1997.5756
Introduction to “Flux-Corrected Transport. I. SHASTA, A Fluid Transport Algorithm That Works”
S. Zalesak (1997)
Numerical Schemes for Conservation Laws
D. Kröner (1997)
10.1006/JCPH.1998.5892
The Runge-Kutta discontinuous Galerkin method for conservation laws V: Multi-D systems
Bernardo Cockburn (1997)
10.1006/JCPH.1997.5700
Flux-Corrected Transport
J. Boris (1997)
10.1016/S0309-1708(96)00033-4
Solution of the advection-dispersion equation in two dimensions by a finite-volume Eulerian-Lagrangian localized adjoint method
R. Healy (1998)
10.1006/JCPH.1998.6032
A DiscontinuoushpFinite Element Method for Diffusion Problems
J. T. Oden (1998)
10.1002/(SICI)1097-0363(19981215)28:9<1325::AID-FLD765>3.0.CO;2-1
Shock capturing viscosities for the general fluid mechanics algorithm
P. Nithiarasu (1998)
The Runge–Kutta discontinuous Galerkin method for conservation laws. I: Multidimensional systems
B Cockburn (1998)
10.1016/S0045-7825(98)00359-4
A discontinuous hp finite element method for convection—diffusion problems
C. Baumann (1999)
10.1006/JCPH.1999.6227
An Analysis of the Discontinuous Galerkin Method for Wave Propagation Problems
F. Hu (1999)
10.1016/S0045-7825(99)00157-7
A free-Lagrange finite element method using space-time elements
P. Hansbo (2000)
10.1088/0957-0233/12/3/704
Vortex methods - theory and practice
Georges-Henri Cottet (2000)
10.1016/S0045-7825(00)00177-8
On stabilized finite element methods for linear systems of convection-diffusion-reaction equations
R. Codina (2000)
10.1016/S0309-1708(01)00051-3
A forward particle tracking Eulerian-Lagrangian localized adjoint method for solution of the contaminant transport equation in three dimensions
P. Binning (2002)
10.1006/JCPH.2002.7180
Toward an oscillation-free, mass conservative, Eulerian-Lagrangian transport model
A. Oliveira (2002)
10.1016/S0377-0427(02)00543-5
Finite element simulation of single crystal growth process using GSMAC method
H. Kohno (2002)
10.1016/S0898-1221(01)00289-9
Grid-free adaptive semi-Lagrangian advection using radial basis functions
J. Behrens (2002)
10.1016/S0045-7825(02)00461-9
An efficient characteristic Galerkin scheme for the advection equation in 3-D
M. Kaazempur-Mofrad (2002)
10.1023/A:1026256231021
Finite Volume Methods for Hyperbolic Problems
R. LeVeque (2002)
10.1115/1.3424474
The finite element method for elliptic problems
P. G. Ciarlet (2002)
Applied CFD Techniques: An Introduction Based on FEM
R. Löhner (2002)
10.1002/NME.602
Time accurate consistently stabilized mesh‐free methods for convection dominated problems
A. Huerta (2003)
10.1109/ICCV.2003.1238357
Meshfree particle method
H. Liu (2003)
10.1016/S0017-9310(03)00301-6
The role of porous media in modeling flow and heat transfer in biological tissues
A. Khaled (2003)
Finite Element Methods for Flow Problems
J. Donea (2003)
10.1016/J.PHYSREP.2003.12.002
Lagrangian fluid description with simple applications in compressible plasma and gas dynamics
H. Schamel (2004)
Meshfree and particle based approaches in computational mechanics
P. Breitkopf (2004)
10.1016/J.JCP.2003.09.017
Power ENO methods: a fifth-order accurate weighted power ENO method
S. Serna (2004)
10.1007/978-3-540-71471-2
Meshfree Particle Methods
Huafeng Liu (2004)
10.1016/J.FUSENGDES.2004.07.013
Progress on the modeling of liquid metal, free surface, MHD flows for fusion liquid walls
Neil B. Morley (2004)
10.1002/NUM.10100
Conservative semi‐Lagrangian advection on adaptive unstructured meshes
A. Iske (2004)
10.1016/J.APNUM.2003.11.002
Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws
L. Krivodonova (2004)
10.1002/FLD.726
Evaluation of discontinuous Galerkin and spectral volume methods for scalar and system conservation laws on unstructured grids
Y. Sun (2004)
10.1016/J.CMA.2004.05.009
High-resolution FEM?FCT schemes for multidimensional conservation laws
D. Kuzmin (2004)
10.1002/NME.1096
The particle finite element method: a powerful tool to solve incompressible flows with free-surfaces and breaking waves
S. Idelsohn (2004)
10.1002/0470013826
Finite Element Methods for Flow Problems: Donea/Flow Problems
J. Donea (2005)
10.1007/3-540-27206-2_6
Algebraic Flux Correction I. Scalar Conservation Laws
D. Kuzmin (2005)
10.1016/J.JBIOMECH.2004.02.037
A CFD level-set method for soft tissue growth: theory and fundamental equations.
M. Lappa (2005)
U . Particle methods
J. Brackbill (2005)
10.1016/J.CES.2005.11.034
Nonlinear, multicomponent, mass transport in porous media
M. Quintard (2006)
10.1016/J.IJHEATMASSTRANSFER.2005.07.045
Comparison of volume-of-fluid methods for surface tension-dominant two-phase flows
D. Gerlach (2006)
10.1016/j.jcp.2005.10.030
A wave-propagation based volume tracking method for compressible multicomponent flow in two space dimensions
Keh-Ming Shyue (2006)



This paper is referenced by
10.1515/phys-2021-0011
Gaussian radial basis functions method for linear and nonlinear convection–diffusion models in physical phenomena
Fuzhang Wang (2021)
10.1016/J.COMPFLUID.2017.09.001
The dual information preserving method for stiff reacting flows
Li Liu (2017)
10.4208/AAMM.2014.M783
Solution of Boundary Value Problems Using Dual Reciprocity Boundary Element Method
Hassan Zakerdoost (2017)
Development of a full particle PIC method for simulating nonlinear wave-structure interaction
Q. Chen (2017)
10.1109/TPS.2016.2609504
An Efficient Semi-Lagrangian Algorithm for Simulation of Corona Discharges: The Position-State Separation Method
L. Liu (2016)
10.1016/J.CMA.2015.11.028
A Lagrangian–Eulerian finite element algorithm for advection–diffusion–reaction problems with phase change
B. Oliveira (2016)
Towards a Simple, Fast, Oscillation-free, High-resolution Algorithm for Convection-Dominated Flows: The Position-State Separation Method
Lipeng Liu (2015)
10.1080/17415977.2014.890609
Comparative numerical analysis of identification problems related to nonlinear transport-diffusion model of a settler
B. Pektas (2015)
An Explicit Characteristic-based Finite Volume-Element Method for Convection-Diffusion-Reaction Equation with Source Term
S. Phongthanapanich (2013)
10.1175/MWR-D-10-05026.1
Trajectory-Tracking Scheme in Lagrangian Form for Solving Linear Advection Problems: Preliminary Tests
L. Dong (2012)
10.1007/S12572-012-0071-1
An explicit characteristic finite volume element method for non-divergence free convection–diffusion-reaction equation
S. Phongthanapanich (2012)
10.1007/S13370-011-0007-0
A generalized 1-dimensional particle transport method for convection diffusion reaction model
James Makungu (2012)
Applying fluid mechanics and Kalman filtering to forecasting electricity spot prices
Anna Shcherbacheva (2011)
A generalized 1D particle transport method for convection diffusion reaction model
Makungu James (2010)
10.1007/S12206-008-1204-0
Combined finite volume and finite element method for convection-diffusion-reaction equation
S. Phongthanapanich (2009)
10.1103/PHYSREVE.79.066113
Dynamic continuum pedestrian flow model with memory effect.
Y. Xia (2009)
10.1016/j.mcm.2008.10.006
Modeling and computer simulation of the identification problem related to the sludge concentration in a settler
B. Pektas (2009)
10.1002/NME.2329
An efficient discontinuous Galerkin method on triangular meshes for a pedestrian flow model
Y. Xia (2008)
10.1016/j.chroma.2008.07.069
Particle transport method for simulation of multicomponent chromatography problems.
O. Shipilova (2008)
Numerical implementation of continuum dislocation-based plasticity
C. Schwarz (2007)
10.1002/FLD.1438
Particle transport method for convection problems with reaction and diffusion
O. Shipilova (2007)
Semantic Scholar Logo Some data provided by SemanticScholar