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Determining the effective resolution of advection schemes. Part II: Numerical testing

James Kent, Christiane Jablonowski, Jared P. Whitehead, Richard B. Rood
2014 Journal of Computational Physics  
Here, a numerical test is developed that can calculate the effective resolution of any scheme (linear or non-linear) for the advection equation.  ...  The tests are focused on the use of non-linear limiters for advection schemes. It is found that the effective resolution of such non-linear schemes is very dependent on the number of time steps.  ...  The work was supported by the Office of Science of the U.S. Department of Energy, Award No. DE-SC0006684. for grid index j. If the flux is spurious then it is limited using δ = 0.  ... 
doi:10.1016/j.jcp.2014.08.045 fatcat:beajbfj4d5htrecqv3yetfzhce

A class of discontinuous Petrov-Galerkin methods. II. Optimal test functions

L. Demkowicz, J. Gopalakrishnan
2010 Numerical Methods for Partial Differential Equations  
Although the question of stable test space choice had attracted the attention of many previous authors, the novelty in our approach lies in the fact we identify a discontinuous Galerkin (DG) framework  ...  Given a trial space, a DPG discretization using its optimal test space counterpart inherits stability from the well-posedness of the undiscretized problem.  ...  value problem, and an approximation space to find numerical solutions, a space of test functions to construct a stable scheme is automatically computed.  ... 
doi:10.1002/num.20640 fatcat:igveoew3xrhdrcftnevk36ocne

Non-hydrostatic semi-elastic hybrid-coordinate SISL extension of HIRLAM. Part II: numerical testing

Rein Rõõm, Aarne Männik, Andres Luhamaa, Marko Zirk
2007 Tellus: Series A, Dynamic Meteorology and Oceanography  
The semi-implicit semi-Lagrangian (SISL), two-time-level, non-hydrostatic numerical scheme, based on the non-hydrostatic, semi-elastic pressure-coordinate equations, is tested in model experiments with  ...  flow over given orography (elliptical hill, mountain ridge, system of successive ridges) in a rectangular domain with emphasis on the numerical accuracy and nonhydrostatic effect presentation capability  ...  In this paper we will report the high-resolution simulation tests with the new numerical model.  ... 
doi:10.3402/tellusa.v59i5.15153 fatcat:webimpb7x5gbjktkhh67wy3go4

Non-hydrostatic semi-elastic hybrid-coordinate SISL extension of HIRLAM. Part II: numerical testing

Rein Rõõm, Aarne Männik, Luhamaa Andres, Zirk Marko
2007 Tellus: Series A, Dynamic Meteorology and Oceanography  
The semi-implicit semi-Lagrangian (SISL), two-time-level, non-hydrostatic numerical scheme, based on the non-hydrostatic, semi-elastic pressure-coordinate equations, is tested in model experiments with  ...  flow over given orography (elliptical hill, mountain ridge, system of successive ridges) in a rectangular domain with emphasis on the numerical accuracy and nonhydrostatic effect presentation capability  ...  In this paper we will report the high-resolution simulation tests with the new numerical model.  ... 
doi:10.1111/j.1600-0870.2007.00253.x fatcat:bh2vrnmfezekpkzaqc6cxgt6zy

Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases - Part I: The O(N) model [article]

Adrian Koenigstein, Martin J. Steil, Nicolas Wink, Eduardo Grossi, Jens Braun, Michael Buballa, Dirk H. Rischke
2021 arXiv   pre-print
The practical application of this approach relies on the derivation of so-called flow equations, which describe the change of the quantum effective action under the variation of a coarse-graining parameter  ...  First of all, we show that this allows to employ powerful numerical techniques developed in the context of fluid dynamics to solve RG equations.  ...  Tests of the UV and IR scales 41 B. Test case II: φ 4 theory 45 1. Results obtained using the KT scheme 45 2. Results obtained using the FRG Taylor (vertex) expansion 47 C.  ... 
arXiv:2108.02504v1 fatcat:czdg577dibhtxnofqp5husemrm

Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases - Part III: Shock and rarefaction waves in RG flows reveal limitations of the N →∞ limit in O(N)-type models [article]

Martin J. Steil, Adrian Koenigstein
2021 arXiv   pre-print
Applying novel analogies between (F)RG flow equations and numerical fluid dynamics from parts I and II of this series of publications, we recast the calculation of expectation values of our toy model into  ...  solving a highly non-linear but exact advection(-diffusion) equation.  ...  physical effects. free QFT in this part of field space.  ... 
arXiv:2108.04037v1 fatcat:h2sdxxa27rgmrim26tmql63srq

Phase-Correcting Data Assimilation and Application to Storm-Scale Numerical Weather Prediction. Part I: Method Description and Simulation Testing

Keith A. Brewster
2003 Monthly Weather Review  
An objective method of determining and correcting phase or position errors in numerical weather prediction is described and tested in a radar data observing system simulation experiment (OSSE) addressing  ...  Such phase or position errors are common in numerical forecasts at grid resolutions of 2-20 km (meso-␥ scale).  ...  The author is grateful for the support and guidance of Dr. Frederick Carr during the development and testing of this concept. Discussions with Drs. Alan Shapiro and Ming Xue contributed to this work.  ... 
doi:10.1175/1520-0493(2003)131<0480:pcdaaa>2.0.co;2 fatcat:zbjw2fbp4vb5jdsnzfumn7c6ya

The Tagus Estuary as a Numerical Modeling Test Bed: A Review

Vaz, Mateus, Pinto, Neves, Dias
2019 Geosciences  
Since the 1980s, the estuary has been a natural laboratory for a great number of multidisciplinary studies, but also a numerical laboratory to test models and to develop new ideas and numerical methodologies  ...  The main objective of this paper is to present a synopsis of the scientific output related to numerical studies in the Tagus system, by reviewing more than fifty papers published over the past four decades  ...  Acknowledgments: The authors acknowledge the contribution of Vanda Brotas and Isabel Ambar for the data depicted in Figure 2 . Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/geosciences10010004 fatcat:3jnfgv34svenxm3ft7vtnv5aru

Numerical tests of evolution systems, gauge conditions, and boundary conditions for 1D colliding gravitational plane waves

J. M. Bardeen, L. T. Buchman
2002 Physical Review D, Particles and fields  
and the longitudinal part of the metric.  ...  We investigate how the accuracy and stability of numerical relativity simulations of 1D colliding plane waves depends on choices of equation formulations, gauge conditions, boundary conditions, and numerical  ...  ACKNOWLEDGMENTS This paper presents the results of one phase of research supported by the NASA Graduate Student Researchers Program under Grant No.  ... 
doi:10.1103/physrevd.65.064037 fatcat:7jclur6z6rbxhb6kizkrpprlbm

Testing the effects of basic numerical implementations of water migration on models of subduction dynamics

M. E. T. Quinquis, S. J. H. Buiter
2014 Solid Earth  
We first test the influence of the water migration scheme using a simple model that simulates the sinking of a cold, hydrated cylinder into a dry, warm mantle.  ...  We aim to show the influence of the numerical scheme of free water migration on the dynamics of the upper mantle and more specifically the mantle wedge.  ...  We acknowledge financial support from the European Commission through Marie-Curie Research Training Network "c2c" (contract MRTN-CT-2006-035957).  ... 
doi:10.5194/se-5-537-2014 fatcat:2cqwtbsqvrakzoysw5z65tc5mi

MOLECULAR LINE EMISSION FROM MULTIFLUID SHOCK WAVES. I. NUMERICAL METHODS AND BENCHMARK TESTS

Glenn E. Ciolek, Wayne G. Roberge
2013 Astrophysical Journal  
solutions and tests showing the convergence of the numerical algorithm.  ...  An exact solution to a MHD Riemann problem forming the basis for an approximate numerical solver used in the homogeneous part of our scheme is presented, along with derivations of the analytic benchmark  ...  The error measure L 1 (v i ) as a function of numerical resolution is provided in Figure 14d ; the data there show for the large part that our code again exhibits second-order accuracy.  ... 
doi:10.1088/0004-637x/768/1/78 fatcat:o6rebgbnj5aypjd2ob2jka4vmu

A depth-averaged debris-flow model that includes the effects of evolving dilatancy. II. Numerical predictions and experimental tests

D. L. George, R. M. Iverson
2014 Proceedings of the Royal Society A  
To solve the equations, we use a shock-capturing numerical scheme with adaptive mesh refinement, implemented in an open-source software package we call D-Claw.  ...  As tests of D-Claw, we compare model output with results from two sets of largescale debris-flow experiments.  ...  Here, we describe mathematical properties of the model, our numerical solution technique, and tests of numerical predictions against experimental data.  ... 
doi:10.1098/rspa.2013.0820 fatcat:b6wtj3a7fzccjewzxzrdbdtuiu

Numerical Model Simulations of a Mesoscale Gravity Wave Event: Sensitivity Tests and Spectral Analyses

Jordan G. Powers
1997 Monthly Weather Review  
Experiments are performed to investigate the effects on wave simulation of upper boundary condition, hydrostatics, vertical and horizontal resolution, and moist physics.  ...  scheme with ice physics, and the Grell cumulus parameterization.  ...  Richard Reed for assistance during the course of this research. Thanks are also extended to Drs. Ying-Hwa Kuo, Richard Rotunno, Dale Durran, Clifford Mass, and K. K.  ... 
doi:10.1175/1520-0493(1997)125<1838:nmsoam>2.0.co;2 fatcat:znzevzov4vg2zgpfjxnwmkp6am

Dynamics of passive tracers in the atmosphere: Laboratory experiments and numerical tests with reanalysis wind fields

Imre M. Jánosi, Péter Kiss, Viktória Homonnai, Margit Pattantyús-Ábrahám, Balázs Gyüre, Tamás Tél
2010 Physical Review E  
Richardson-Obukhov scaling ͑superdiffusion with an exponent value of 3/2͒ is neither observed in the laboratory nor in the numerical tests.  ...  Laboratory and numerical experiments are reported on dye advection processes in geostrophic turbulence.  ...  of the reanalysis wind field in the numerical tests.  ... 
doi:10.1103/physreve.82.046308 pmid:21230391 fatcat:idgt3ousojhjxnvxppr2xr43bu

Relativistic radiation magnetohydrodynamics in dynamical spacetimes: Numerical methods and tests

Brian D. Farris, Tsz Ka Li, Yuk Tung Liu, Stuart L. Shapiro
2008 Physical Review D  
We evolve the metric by integrating the BSSN equations, and use a conservative, high-resolution shock-capturing scheme to evolve both the MHD and radiation moment equations.  ...  good agreement between analytic and numerical solutions.  ...  The goal of this part of the numerical evolution is to determine the fundamental "primitive" variables P ≡ (ρ 0 , P, v i , B i , E, F i ) at future times, given initial values of P.  ... 
doi:10.1103/physrevd.78.024023 fatcat:75ycflhearas7dgfdirra5xsa4
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