Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/energy-transfers-in-atmosphere-and-ocean-reducing-spurious-diapycnal-P1AS5n09LJ
References (94)
-
E. Harabetian (1986)
A convergent series expansion for hyperbolic systems of conservation lawsTransactions of the American Mathematical Society, 294
-
L. Urakawa, H. Hasumi (2014)
Effect of numerical diffusion on the water mass transformation in eddy-resolving modelsOcean Modelling, 74
-
R. LeVeque (2002)
Finite Volume Methods for Hyperbolic Problems: Characteristics and Riemann Problems for Linear Hyperbolic Equations -
Jianzhen Qian, Jiequan Li, Shuanghu Wang (2014)
The generalized Riemann problems for compressible fluid flows: Towards high orderJ. Comput. Phys., 259
-
Alexander Shchepetkin, J. McWilliams (1998)
Quasi-Monotone Advection Schemes Based on Explicit Locally Adaptive DissipationMonthly Weather Review, 126
-
J. Donea, A. Huerta (2003)
Finite Element Methods for Flow Problems -
M. Ben-Artzi, Jiequan Li (2007)
Hyperbolic balance laws: Riemann invariants and the generalized Riemann problemNumerische Mathematik, 106
-
D. Webb, B. Cuevas, C. Richmond (1998)
IMPROVED ADVECTION SCHEMES FOR OCEAN MODELSJournal of Atmospheric and Oceanic Technology, 15
-
A. Bressan (2000)
Hyperbolic systems of conservation laws : the one-dimensional Cauchy problem, 20
-
J. Getzlaff (2008)
Diagnostics of diapycnal diffusion in z-level ocean models -
E. Toro (2016)
The Riemann Problem: Solvers and Numerical Fluxes, 17
-
A. Bourgeade, P. Floch, P. Raviart (1989)
An asymptotic expansion for the solution of the generalized Riemann problem. Part 2 : application to the equations of gas dynamicsAnnales De L Institut Henri Poincare-analyse Non Lineaire, 6
-
M. Petersen, D. Jacobsen, T. Ringler, M. Hecht, M. Maltrud (2015)
Evaluation of the arbitrary Lagrangian–Eulerian vertical coordinate method in the MPAS-Ocean modelOcean Modelling, 86
-
H. Burchard (2012)
Quantification of numerically induced mixing and dissipation in discretisations of shallow water equationsGEM - International Journal on Geomathematics, 3
-
F. Lörcher, G. Gassner, C. Munz (2007)
A Discontinuous Galerkin Scheme Based on a Space–Time Expansion. I. Inviscid Compressible Flow in One Space DimensionJournal of Scientific Computing, 32
-
A. Harten, B. Engquist, S. Osher, S. Chakravarthy (1987)
Uniformly high order accurate essentially non-oscillatory schemes, 111Journal of Computational Physics, 71
-
M. Ben-Artzi, J. Falcovitz, Jiequan Li (2008)
THE CONVERGENCE OF THE GRP SCHEMEDiscrete and Continuous Dynamical Systems, 23
-
R. Timmermann, Qiang Wang, H. Hellmer (2012)
Ice-shelf basal melting in a global finite-element sea-ice/ice-shelf/ocean modelAnnals of Glaciology, 53
-
Qiang Wang, S. Danilov, D. Sidorenko, R. Timmermann, C. Wekerle, Xuezhu Wang, T. Jung, J. Schröter (2014)
The Finite Element Sea Ice-Ocean Model (FESOM) v.1.4: formulation of an ocean general circulation modelGeoscientific Model Development, 7
-
Tatsien Li, Libin Wang (2002)
Global Propagation of Regular Nonlinear Hyperbolic Waves -
D. Balsara, C. Meyer, M. Dumbser, H. Du, Zhiliang Xu (2010)
Efficient implementation of ADER schemes for Euler and magnetohydrodynamical flows on structured meshes - Speed comparisons with Runge-Kutta methodsJ. Comput. Phys., 235
-
H. Wendland (2004)
Scattered Data Approximation -
K. Klingbeil, H. Burchard (2013)
Implementation of a direct nonhydrostatic pressure gradient discretisation into a layered ocean modelOcean Modelling, 65
-
E. Toro, V. Titarev (2006)
Derivative Riemann solvers for systems of conservation laws and ADER methodsJ. Comput. Phys., 212
-
E. Toro, G. Montecinos (2015)
Implicit, semi-analytical solution of the generalized Riemann problem for stiff hyperbolic balance lawsJ. Comput. Phys., 303
-
M. Mohammadi-Aragh, K. Klingbeil, N. Brüggemann, C. Eden, H. Burchard (2015)
The impact of advection schemes on restratifiction due to lateral shear and baroclinic instabilitiesOcean Modelling, 94
-
F. Lemarié, L. Debreu, Alexander Shchepetkin, J. McWilliams (2012)
On the stability and accuracy of the harmonic and biharmonic isoneutral mixing operators in ocean modelsOcean Modelling, 52
-
S. Griffies, R. Pacanowski, R. Hallberg (2000)
Spurious Diapycnal Mixing Associated with Advection in a z-Coordinate Ocean ModelMonthly Weather Review, 128
-
M. Prather (1986)
Numerical advection by conservation of second-order moments. [for trace element spatial distribution and chemical interaction in atmosphere] -
S. Godunov, I. Bohachevsky (1959)
Finite difference method for numerical computation of discontinuous solutions of the equations of fluid dynamics -
O. Zanotti, M. Dumbser (2015)
Efficient conservative ADER schemes based on WENO reconstruction and space-time predictor in primitive variablesComputational Astrophysics and Cosmology, 3
-
R. Warming, B. Hyett (1974)
The modified equation approach to the stability and accuracy analysis of finite-difference methodsJournal of Computational Physics, 14
-
Tatsien Li, Wen-ci Yu (1985)
Boundary value problems for quasilinear hyperbolic systems -
Bkam Leer, B. Leer (1979)
Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's methodJournal of Computational Physics, 32
-
Matthieu Leclair, G. Madec (2011)
z˜-Coordinate, an Arbitrary Lagrangian–Eulerian coordinate separating high and low frequency motionsOcean Modelling, 37
-
T. Aboiyar, E. Georgoulis, A. Iske (2010)
Adaptive ADER Methods Using Kernel-Based Polyharmonic Spline WENO ReconstructionSIAM J. Sci. Comput., 32
-
M. Buhmann (2003)
Radial Basis Functions: Theory and Implementations: Bibliography -
R. Abgrall (1994)
On essentially non-oscillatory schemes on unstructured meshes: analysis and implementationJournal of Computational Physics, 114
-
O. Zanotti, F. Fambri, M. Dumbser (2015)
Solving the relativistic magnetohydrodynamics equations with ADER discontinuous Galerkin methods, a posteriori subcell limiting and adaptive mesh refinementMonthly Notices of the Royal Astronomical Society, 452
-
M. Dumbser, C. Enaux, E. Toro (2008)
Finite volume schemes of very high order of accuracy for stiff hyperbolic balance lawsJ. Comput. Phys., 227
-
C. Dafermos (2000)
Hyberbolic Conservation Laws in Continuum Physics -
J. Getzlaff, G. Nurser, A. Oschlies (2010)
Diagnostics of diapycnal diffusivity in z-level ocean models part I: 1-Dimensional case studiesOcean Modelling, 35
-
Claus Goetz, M. Dumbser (2016)
A Novel Solver for the Generalized Riemann Problem Based on a Simplified LeFloch–Raviart Expansion and a Local Space–Time Discontinuous Galerkin FormulationJournal of Scientific Computing, 69
-
A. Iske (2007)
Particle Flow Simulation by Using Polyharmonic Splines -
W. Boscheri, D. Balsara, M. Dumbser (2013)
Lagrangian ADER-WENO finite volume schemes on unstructured triangular meshes based on genuinely multidimensional HLL Riemann solversJ. Comput. Phys., 267
-
J. Duchon (1976)
Splines minimizing rotation-invariant semi-norms in Sobolev spaces -
R. Hofmeister, H. Burchard, J. Beckers (2010)
Non-uniform adaptive vertical grids for 3D numerical ocean modelsOcean Modelling, 33
-
T. Ringler, M. Petersen, R. Higdon, D. Jacobsen, Philip Jones, M. Maltrud (2013)
A multi-resolution approach to global ocean modelingOcean Modelling, 69
-
G. Gassner, F. Lörcher, C. Munz (2008)
A Discontinuous Galerkin Scheme based on a Space-Time Expansion II. Viscous Flow Equations in Multi DimensionsJournal of Scientific Computing, 34
-
K. Klingbeil, J. Becherer, E. Schulz, H. Swart, H. Schuttelaars, A. Valle‐Levinson, H. Burchard (2019)
Thickness-Weighted Averaging in Tidal Estuaries and the Vertical Distribution of the Eulerian Residual TransportJournal of Physical Oceanography
-
D. Sidorenko, T. Rackow, T. Jung, T. Semmler, D. Barbi, S. Danilov, K. Dethloff, W. Dorn, K. Fieg, H. Goessling, D. Handorf, S. Harig, W. Hiller, S. Juricke, M. Losch, J. Schröter, D. Sein, Qiang Wang (2015)
Towards multi-resolution global climate modeling with ECHAM6–FESOM. Part I: model formulation and mean climateClimate Dynamics, 44
-
Steven Hanna (2003)
Generalized Riemann Problems in Computational Fluid Dynamics. By M. BEN-ARTZI & J. FALCOVITZ. Cambridge University Press, 2003. 366 pp. ISBN 0 521 77296 6. £ 55 or $75Journal of Fluid Mechanics, 497
-
F. Lemarié, J. Kurian, Alexander Shchepetkin, M. Molemaker, F. Colas, J. McWilliams (2012)
Are there inescapable issues prohibiting the use of terrain-following coordinates in climate models?Ocean Modelling, 42
-
M. Ilıcak (2016)
Quantifying spatial distribution of spurious mixing in ocean modelsOcean Modelling, 108
-
K. Klingbeil, M. Mohammadi-Aragh, U. Gräwe, H. Burchard (2014)
Quantification of spurious dissipation and mixing – Discrete variance decay in a Finite-Volume frameworkOcean Modelling, 81
-
S. Danilov, D. Sidorenko, Qiang Wang, T. Jung (2016)
The Finite-volumE Sea ice–Ocean Model (FESOM2)Geoscientific Model Development, 10
-
E. Toro, V. Titarev (2002)
Solution of the generalized Riemann problem for advection–reaction equationsProceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 458
-
G. Montecinos, C. Castro, M. Dumbser, E. Toro (2012)
Comparison of solvers for the generalized Riemann problem for hyperbolic systems with source termsJ. Comput. Phys., 231
-
H. Burchard, H. Rennau (2008)
Comparative quantification of physically and numerically induced mixing in ocean modelsOcean Modelling, 20
-
W. Skamarock, A. Gassmann (2011)
Conservative Transport Schemes for Spherical Geodesic Grids: High-Order Flux Operators for ODE-Based Time IntegrationMonthly Weather Review, 139
-
A. Adcroft, R. Hallberg (2006)
On methods for solving the oceanic equations of motion in generalized vertical coordinatesOcean Modelling, 11
-
H. Burchard, J. Beckers (2004)
Non-uniform adaptive vertical grids in one-dimensional numerical ocean modelsOcean Modelling, 6
-
G. Gassner, M. Dumbser, F. Hindenlang, C. Munz (2011)
Explicit one-step time discretizations for discontinuous Galerkin and finite volume schemes based on local predictorsJ. Comput. Phys., 230
-
Claus Goetz, A. Iske (2015)
Approximate solutions of generalized Riemann problems for nonlinear systems of hyperbolic conservation lawsMath. Comput., 85
-
Y. Nakayama, R. Timmermann, M. Schröder, H. Hellmer (2014)
On the difficulty of modeling Circumpolar Deep Water intrusions onto the Amundsen Sea continental shelfOcean Modelling, 84
-
P. Lax (1957)
Hyperbolic systems of conservation laws IICommunications on Pure and Applied Mathematics, 10
-
C. Hirt (1968)
Heuristic stability theory for finite-difference equations☆Journal of Computational Physics, 2
-
M. Ilıcak, A. Adcroft, S. Griffies, R. Hallberg (2012)
Spurious dianeutral mixing and the role of momentum closureOcean Modelling, 45
-
P. Floch, P. Raviart (1988)
An asymptotic expansion for the solution of the generalized Riemann problem Part I: General theoryAnnales De L Institut Henri Poincare-analyse Non Lineaire, 5
-
Zhicheng Yang, Huazhong Tang (2012)
A direct Eulerian GRP scheme for relativistic hydrodynamics: Two-dimensional caseJ. Comput. Phys., 231
-
C. Castro, E. Toro (2008)
Solvers for the high-order Riemann problem for hyperbolic balance lawsJ. Comput. Phys., 227
-
S. Danilov (2013)
Ocean modeling on unstructured meshes -
E. Toro (1997)
Riemann Solvers and Numerical Methods for Fluid Dynamics -
W. Boscheri, M. Dumbser (2014)
A direct Arbitrary-Lagrangian-Eulerian ADER-WENO finite volume scheme on unstructured tetrahedral meshes for conservative and non-conservative hyperbolic systems in 3DJ. Comput. Phys., 275
-
W. Boscheri, M. Dumbser (2013)
Arbitrary-Lagrangian-Eulerian One-Step WENO Finite Volume Schemes on Unstructured Triangular MeshesarXiv: Numerical Analysis
-
H. Wan, M. Giorgetta, G. Zängl, M. Restelli, D. Majewski, Luca Bonaventura, Kristina Frohlich, D. Reinert, P. Rípodas, L. Kornblueh, J. Förstner (2013)
The ICON-1.2 hydrostatic atmospheric dynamical core on triangular grids – Part 1: Formulation and performance of the baseline versionGeoscientific Model Development, 6
-
Alexander Shchepetkin, J. McWilliams (2009)
Correction and commentary for "Ocean forecasting in terrain-following coordinates: Formulation and skill assessment of the regional ocean modeling system" by Haidvogel et al., J. Comp. Phys 227, pp 3595-3624J. Comput. Phys., 228
-
A. Iske (2013)
On the Construction of Kernel-Based Adaptive Particle Methods in Numerical Flow Simulation -
K. Klingbeil, F. Lemarié, L. Debreu, H. Burchard (2018)
The numerics of hydrostatic structured-grid coastal ocean models: state of the art and future perspectivesOcean Modelling, 125
-
M. Maqueda, G. Holloway (2006)
Second-order moment advection scheme applied to Arctic Ocean simulationOcean Modelling, 14
-
W. Boscheri, M. Dumbser, D. Balsara (2013)
High‐order ADER‐WENO ALE schemes on unstructured triangular meshes—application of several node solvers to hydrodynamics and magnetohydrodynamicsInternational Journal for Numerical Methods in Fluids, 76
-
A. Gibson, A. Hogg, A. Kiss, C. Shakespeare, A. Adcroft (2017)
Attribution of horizontal and vertical contributions to spurious mixing in an Arbitrary Lagrangian-Eulerian ocean modelOcean Modelling, 119
-
M. Dumbser, M. Käser (2007)
Arbitrary high order non-oscillatory finite volume schemes on unstructured meshes for linear hyperbolic systemsJ. Comput. Phys., 221
-
V. Titarev, E. Toro (2002)
ADER: Arbitrary High Order Godunov ApproachJournal of Scientific Computing, 17
-
M. Ben-Artzi, J. Falcovitz (1984)
A second-order Godunov-type scheme for compressible fluid dynamicsJournal of Computational Physics, 55
-
J. Donea, A. Huerta, J. Ponthot, A. Rodríguez‐Ferran (2004)
Arbitrary Lagrangian–Eulerian Methods -
J. Smoller (1983)
Shock Waves and Reaction-Diffusion Equations -
U. Gräwe, P. Holtermann, K. Klingbeil, H. Burchard (2015)
Advantages of vertically adaptive coordinates in numerical models of stratified shelf seasOcean Modelling, 92
-
M. Ben-Artzi, Jiequan Li, G. Warnecke (2006)
A direct Eulerian GRP scheme for compressible fluid flowsJ. Comput. Phys., 218
-
E. Toro, R. Millington, L. Nejad (2001)
Towards Very High Order Godunov Schemes -
M. Dumbser, I. Peshkov, E. Romenski, O. Zanotti (2015)
High order ADER schemes for a unified first order hyperbolic formulation of continuum mechanics: Viscous heat-conducting fluids and elastic solidsJ. Comput. Phys., 314
-
C. Hill, D. Ferreira, J. Campin, J. Marshall, R. Abernathey, N. Barrier (2012)
Controlling spurious diapycnal mixing in eddy-resolving height-coordinate ocean models – Insights from virtual deliberate tracer release experimentsOcean Modelling, 45
-
M. Dumbser, D. Balsara, E. Toro, C. Munz (2008)
A unified framework for the construction of one-step finite volume and discontinuous Galerkin schemes on unstructured meshesJ. Comput. Phys., 227
-
I. Abalakin, A. Dervieux, Tatiana Kozubskaya (2002)
A vertex centered high order MUSCL scheme applying to linearised Euler acoustics
- Publisher
- Springer International Publishing
- Copyright
- © Springer Nature Switzerland AG 2019
- ISBN
- 978-3-030-05703-9
- Pages
- 245 –286
- DOI
- 10.1007/978-3-030-05704-6_8
- Publisher site
- See Chapter on Publisher Site
Abstract
[Transport algorithms of numerical ocean circulation models are frequently exhibiting truncation errors leading to spurious diapycnal mixing of water masses. This chapter discusses methods that might be useful in diagnosing spurious diapycnal mixing and describes some approaches that might be helpful for its reduction. The first one is related to the use of the Arbitrary Lagrangian Eulerian (ALE) vertical coordinate which allows the implementation of vertically moving meshes that may partly follow the isopycnals even if the basic vertical coordinate differs from isopycnal. The second approach relies on modified advection schemes with the dissipative part of the transport operators directed isopycnally. Finally the third approach deals with new efficient and stable advection algorithms of arbitrary high order based on the WENO-ADER method, which can be applied to both structured and unstructured meshes. While practical benefits of using the reviewed approaches depend on applications, there are indications that equipping present state-of-the-art ocean circulation models with them would lead to reduced spurious transformations.]
Published: Jan 24, 2019