The analytical solution of the Riemann problem in relativistic hydrodynamics

1994 ◽  
Vol 258 ◽  
pp. 317-333 ◽  
Author(s):  
José Ma Martí ◽  
Ewald Müller
Keyword(s):  
High Resolution ◽  
Analytical Solution ◽  
Riemann Problem ◽  
Shock Capturing ◽  
Relativistic Hydrodynamics ◽  
Minkowski Space Time ◽  
Intermediate States ◽  
Relativistic Flow ◽  
Initial Discontinuity ◽  
The Impact

We consider the decay of an initial discontinuity in a polytropic gas in a Minkowski space–time (the special relativistic Riemann problem). In order to get a general analytical solution for this problem, we analyse the properties of the relativistic flow across shock waves and rarefactions. As in classical hydrodynamics, the solution of the Riemann problem is found by solving an implicit algebraic equation which gives the pressure in the intermediate states. The solution presented here contains as a particular case the special relativistic shock-tube problem in which the gas is initially at rest. Finally, we discuss the impact of this result on the development of high-resolution shock-capturing numerical codes to solve the equations of relativistic hydrodynamics.

scholarly journals Long GRBs and Supernovae from Collapsars

2005 ◽  
Vol 192 ◽  
pp. 417-423
Author(s):  
A.I. MacFadyen
Keyword(s):  
High Resolution ◽  
Adaptive Mesh Refinement ◽  
Gamma Ray ◽  
Massive Stars ◽  
Mesh Refinement ◽  
Adaptive Mesh ◽  
Gamma Ray Bursts ◽  
Relativistic Hydrodynamics ◽  
Long Duration ◽  
Relativistic Flow

SummaryLong duration gamma-ray bursts are associated with the death of massive stars as earlier observations and theoretical arguments had suggested. Supernova 2003dh observed with GRB030329 confirms this picture. Current progress in developing numerical special relativistic hydrodynamics codes with adaptive mesh refinement is allowing for high-resolution simulations of relativistic flow relevant for simulations of GRBs.

scholarly journals The exact solution of the Riemann problem with non-zero tangential velocities in relativistic hydrodynamics

2000 ◽  
Vol 422 ◽  
pp. 125-139 ◽  
Author(s):  
JOSÉ A. PONS ◽  
JOSÉ Ma MARTÍ ◽  
EWALD MÜLLER
Keyword(s):  
Riemann Problem ◽  
The Self ◽  
Relativistic Hydrodynamics ◽  
Relativistic Hydrodynamic ◽  
Jump Conditions ◽  
Normal Flow ◽  
Rarefaction Waves ◽  
Self Similarity ◽  
Similarity Condition ◽  
The Impact

We have generalized the exact solution of the Riemann problem in special relativistic hydrodynamics (Martí & Müller 1994) for arbitrary tangential flow velocities. The solution is obtained by solving the jump conditions across shocks plus an ordinary differential equation arising from the self-similarity condition along rarefaction waves, in a similar way as in purely normal flow. The dependence of the solution on the tangential velocities is analysed, and the impact of this result on the development of multi-dimensional relativistic hydrodynamic codes (of Godunov type) is discussed.

A HIGH ORDER KINETIC FLUX-SPLITTING METHOD FOR THE SPECIAL RELATIVISTIC HYDRODYNAMICS

2005 ◽  
Vol 02 (01) ◽  
pp. 49-74 ◽  
Author(s):  
SHAMSUL QAMAR ◽  
GERALD WARNECKE
Keyword(s):  
High Resolution ◽  
Kinetic Theory ◽  
Splitting Method ◽  
High Order ◽  
Shock Capturing ◽  
High Order Accuracy ◽  
Order Kinetic ◽  
Relativistic Hydrodynamics ◽  
Order Accuracy ◽  
Flux Splitting

In this article we present a flux splitting method based on gas-kinetic theory for the special relativistic hydrodynamics (SRHD) [Landau and Lifshitz, Fluid Mechanics, Pergamon New York, 1987] in one and two space dimensions. This kinetic method is based on the direct splitting of the macroscopic flux functions with the consideration of particle transport. At the same time, particle "collisions" are implemented in the free transport process to reduce numerical dissipation. Due to the nonlinear relations between conservative and primitive variables and the consequent complexity of the Jacobian matrix, the multi-dimensional shock-capturing numerical schemes for SRHD are computationally more expensive. All the previous methods presented for the solution of these equations were based on the macroscopic continuum description. These upwind high-resolution shock-capturing (HRSC) schemes, which were originally made for non-relativistic flows, were extended to SRHD. However our method, which is based on kinetic theory is more related to the physics of these equations and is very efficient, robust, and easy to implement. In order to get high order accuracy in space, we use a third order central weighted essentially non-oscillatory (CWENO) finite difference interpolation routine. To achieve high order accuracy in time we use a Runge-Kutta time stepping method. The one- and two-dimensional computations reported in this paper show the desired accuracy, high resolution, and robustness of the method.

Atomic resolution characterisation of interface structures by Electron Energy Loss Spectroscopy

1993 ◽  
Vol 51 ◽  
pp. 576-577
Author(s):  
N. D. Browning ◽  
M. M. McGibbon ◽  
M. F. Chisholm ◽  
S. J. Pennycook
Keyword(s):  
High Resolution ◽  
Energy Loss ◽  
Electron Energy ◽  
Electron Energy Loss Spectroscopy ◽  
Imaging Technique ◽  
Atomic Scale ◽  
Atomic Resolution ◽  
Reference Image ◽  
The Impact ◽  
Electron Energy Loss

The recent development of the Z-contrast imaging technique for the VG HB501 UX dedicated STEM, has added a high-resolution imaging facility to a microscope used mainly for microanalysis. This imaging technique not only provides a high-resolution reference image, but as it can be performed simultaneously with electron energy loss spectroscopy (EELS), can be used to position the electron probe at the atomic scale. The spatial resolution of both the image and the energy loss spectrum can be identical, and in principle limited only by the 2.2 Å probe size of the microscope. There now exists, therefore, the possibility to perform chemical analysis of materials on the scale of single atomic columns or planes.In order to achieve atomic resolution energy loss spectroscopy, the range over which a fast electron can cause a particular excitation event, must be less than the interatomic spacing. This range is described classically by the impact parameter, b, which ranges from ~10 Å for the low loss region of the spectrum to <1Å for the core losses.

High-Resolution Climate Change Impact Analysis on Expected Future Water Availability in the Upper Jordan Catchment and the Middle East

2014 ◽  
Vol 15 (4) ◽  
pp. 1517-1531 ◽  
Author(s):  
Gerhard Smiatek ◽  
Harald Kunstmann ◽  
Andreas Heckl
Keyword(s):  
Climate Change ◽  
High Resolution ◽  
Water Availability ◽  
Impact Analysis ◽  
River Flow ◽  
Climate Model ◽  
Mesoscale Model ◽  
Global Climate Model ◽  
Full Range ◽  
The Impact

Abstract The impact of climate change on the future water availability of the upper Jordan River (UJR) and its tributaries Dan, Snir, and Hermon located in the eastern Mediterranean is evaluated by a highly resolved distributed approach with the fifth-generation Pennsylvania State University–NCAR Mesoscale Model (MM5) run at 18.6- and 6.2-km resolution offline coupled with the Water Flow and Balance Simulation Model (WaSiM). The MM5 was driven with NCEP reanalysis for 1971–2000 and with Hadley Centre Coupled Model, version 3 (HadCM3), GCM forcings for 1971–2099. Because only one regional–global climate model combination was applied, the results may not give the full range of possible future projections. To describe the Dan spring behavior, the hydrological model was extended by a bypass approach to allow the fast discharge components of the Snir to enter the Dan catchment. Simulation results for the period 1976–2000 reveal that the coupled system was able to reproduce the observed discharge rates in the partially karstic complex terrain to a reasonable extent with the high-resolution 6.2-km meteorological input only. The performed future climate simulations show steadily rising temperatures with 2.2 K above the 1976–2000 mean for the period 2031–60 and 3.5 K for the period 2070–99. Precipitation trends are insignificant until the middle of the century, although a decrease of approximately 12% is simulated. For the end of the century, a reduction in rainfall ranging between 10% and 35% can be expected. Discharge in the UJR is simulated to decrease by 12% until 2060 and by 26% until 2099, both related to the 1976–2000 mean. The discharge decrease is associated with a lower number of high river flow years.

Splash formation by spherical drops

2001 ◽  
Vol 427 ◽  
pp. 73-105 ◽  
Author(s):  
LIOW JONG LENG
Keyword(s):  
High Resolution ◽  
Quantitative Data ◽  
Water Surface ◽  
High Speed ◽  
Scaling Laws ◽  
Capillary Wave ◽  
Water Drop ◽  
Qualitative And Quantitative ◽  
High Resolution Images ◽  
The Impact

The impact of a spherical water drop onto a water surface has been studied experimentally with the aid of a 35 mm drum camera giving high-resolution images that provided qualitative and quantitative data on the phenomena. Scaling laws for the time to reach maximum cavity sizes have been derived and provide a good fit to the experimental results. Transitions between the regimes for coalescence-only, the formation of a high-speed jet and bubble entrapment have been delineated. The high-speed jet was found to occur without bubble entrapment. This was caused by the rapid retraction of the trough formed by a capillary wave converging to the centre of the cavity base. The converging capillary wave has a profile similar to a Crapper wave. A plot showing the different regimes of cavity and impact drop behaviour in the Weber–Froude number-plane has been constructed for Fr and We less than 1000.

scholarly journals The Impact of Forcing Datasets on the High-Resolution Simulation of Tropical Storm Ivan (2004) in the Southern Appalachians

2012 ◽  
Vol 140 (10) ◽  
pp. 3300-3326 ◽  
Author(s):  
Xiaoming Sun ◽  
Ana P. Barros
Keyword(s):  
High Resolution ◽  
Global Analysis ◽  
Surface Wind ◽  
Tropical Storm ◽  
Southern Appalachians ◽  
Low Level ◽  
Simulated Precipitation ◽  
Forced Simulation ◽  
The Impact ◽  
Resolution Simulation

Abstract The influence of large-scale forcing on the high-resolution simulation of Tropical Storm Ivan (2004) in the southern Appalachians was investigated using the Weather Research and Forecasting model (WRF). Two forcing datasets were employed: the North American Regional Reanalysis (NARR; 32 km × 32 km) and the NCEP Final Operational Global Analysis (NCEP FNL; 1° × 1°). Simulated fields were evaluated against rain gauge, radar, and satellite data; sounding observations; and the best track from the National Hurricane Center (NHC). Overall, the NCEP FNL forced simulation (WRF_FNL) captures storm structure and evolution more accurately than the NARR forced simulation (WRF_NARR), benefiting from the hurricane initialization scheme in the NCEP FNL. Further, the performance of WRF_NARR is also negatively affected by a previously documented low-level warm bias in NARR. These factors lead to excessive precipitation in the Piedmont region, delayed rainfall in Alabama, as well as spatially displaced and unrealistically extreme rainbands during its passage over the southern Appalachians. Spatial filtering of the simulated precipitation fields confirms that the storm characteristics inherited from the forcing are critical to capture the storm’s impact at local places. Compared with the NHC observations, the storm is weaker in both NARR and NCEP FNL (up to Δp ~ 5 hPa), yet it is persistently deeper in all WRF simulations forced by either dataset. The surface wind fields are largely overestimated. This is attributed to the underestimation of surface roughness length over land, leading to underestimation of surface drag, reducing low-level convergence, and weakening the dissipation of the simulated cyclone.

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