High-resolution shock capturing scheme for ideal hydrodynamics in general relativity optimized for quasistationary solutions

2006 ◽  
Vol 74 (12) ◽  
Author(s):  
Wolfgang Kastaun
Keyword(s):  
General Relativity ◽  
High Resolution ◽  
Shock Capturing ◽  
Quasistationary Solutions

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.

Conservative Formulation of Large Deformation Plasticity

1993 ◽  
Vol 46 (12) ◽  
pp. 519-526 ◽  
Author(s):  
James G. Glimm ◽  
Bradley J. Plohr ◽  
David H. Sharp
Keyword(s):  
High Resolution ◽  
Shear Band ◽  
Large Deformation ◽  
Large Deformations ◽  
Shear Bands ◽  
Shock Capturing ◽  
Jump Discontinuity ◽  
Governing Equations ◽  
Conservative Form ◽  
Deformation Plasticity

We explain several ideas which may, either singly or in combination, help achieve high resolution in simulations of large-deformation plasticity. Because of the large deformations, we work in the Eulerian picture. The governing equations are written in a fully conservative form, which are correct for discontinuous as well as continuous solutions. Models of shear bands are discussed. These models describe the internal dynamics of a developed shear band in terms of time-asymptotic states; in other words, the smooth internal structure is replaced by a jump discontinuity, and the shear band evolution is determined by jump relations. This analysis is useful for high resolution numerical methods, including both shock capturing and shock tracking schemes, as well as for the understanding and validation of computations, independently of the underlying method. Preliminary computations, which illustrate the feasibility of these ideas, are presented.

scholarly journals Coastal flooding of urban areas by overtopping: dynamic modelling application to the Johanna storm (2008) in Gâvres (France)

2015 ◽  
Vol 15 (11) ◽  
pp. 2497-2510 ◽  
Author(s):  
S. Le Roy ◽  
R. Pedreros ◽  
C. André ◽  
F. Paris ◽  
S. Lecacheux ◽  
...  
Keyword(s):  
High Resolution ◽  
Urban Area ◽  
Urban Areas ◽  
Digital Terrain Model ◽  
Time Dependent ◽  
Shock Capturing ◽  
Terrain Model ◽  
Digital Terrain ◽  
Very High ◽  
Water Depths

Abstract. Recent dramatic events have allowed significant progress to be achieved in coastal flood modelling over recent years. Classical approaches generally estimate wave overtopping by means of empirical formulas or 1-D simulations, and the flood is simulated on a DTM (digital terrain model), using soil roughness to characterize land use. The limits of these methods are typically linked to the accuracy of overtopping estimation (spatial and temporal distribution) and to the reliability of the results in urban areas, which are places where the assets are the most crucial. This paper intends to propose and apply a methodology to simulate simultaneously wave overtopping and the resulting flood in an urban area at a very high resolution. This type of 2-D simulation presents the advantage of allowing both the chronology of the storm and the particular effect of urban areas on the flows to be integrated. This methodology is based on a downscaling approach, from regional to local scales, using hydrodynamic simulations to characterize the sea level and the wave spectra. A time series is then generated including the evolutions of these two parameters, and imposed upon a time-dependent phase-resolving model to simulate the overtopping over the dike. The flood is dynamically simulated directly by this model: if the model uses adapted schemes (well balanced, shock capturing), the calculation can be led on a DEM (digital elevation model) that includes buildings and walls, thereby achieving a realistic representation of the urban areas. This methodology has been applied to an actual event, the Johanna storm (10 March 2008) in Gâvres (South Brittany, in western France). The use of the SURF-WB model, a very stable time-dependent phase-resolving model using non-linear shallow water equations and well-balanced shock-capturing schemes, allowed simulating both the dynamics of the overtopping and the flooding in the urban area, taking into account buildings and streets thanks to a very high resolution (1 m). The results obtained proved to be very coherent with the available reports in terms of overtopping sectors, flooded area, water depths and chronology. This method makes it possible to estimate very precisely not only the overtopping flows, but also the main characteristics of flooding in a complex topography like an urban area, and indeed the hazard at a very high resolution (water depths and vertically integrated current speeds). The comparison with a similar flooding simulation using a more classical approach (a digital terrain model with no buildings, and a representation of the urban area by an increased soil roughness) has allowed the advantages of an explicit representation of the buildings and the streets to be identified: if, in the studied case, the impact of the urbanization representation on water levels does indeed remain negligible, the flood dynamics and the current speeds can be considerably underestimated when no explicit representation of the buildings is provided, especially along the main streets. Moreover, on the seaside, recourse to a time-dependent phase-resolving model using non-stationary conditions allows a better representation of the flows caused by overtopping. Finally, this type of simulation is shown to be of value for hazard studies, thanks to the high level of accuracy of the results in urban areas where assets are concentrated. This methodology, although it is currently still quite difficult to implement and costly in terms of calculation time, can expect to be increasingly resorted to in years to come, thanks to the recent developments in wave models and to the increasing availability of LiDAR data.

scholarly journals High-resolution shock-capturing numerical simulations of three-phase immiscible fluids from the unsaturated to the saturated zone

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Alessandra Feo ◽  
Fulvio Celico
Keyword(s):  
Fluid Flow ◽  
High Resolution ◽  
Capillary Pressure ◽  
Immiscible Fluids ◽  
Shock Capturing ◽  
Immiscible Fluid ◽  
Saturated Zone ◽  
Time Step ◽  
Three Phase ◽  
Sharp Front

AbstractNumerical modeling of immiscible contaminant fluid flow in unsaturated and saturated porous aquifers is of great importance in many scientific fields to properly manage groundwater resources. We present a high-resolution numerical model that simulates three-phase immiscible fluid flow in both unsaturated and saturated zone in a porous aquifer. We use coupled conserved mass equations for each phase and study the dynamics of a multiphase fluid flow as a function of saturation, capillary pressure, permeability, and porosity of the different phases, initial and boundary conditions. To deal with the sharp front originated from the partial differential equations’ nonlinearity and accurately propagate the sharp front of the fluid component, we use a high-resolution shock-capturing method to treat discontinuities due to capillary pressure and permeabilities that depend on the saturation of the three different phases. The main approach to the problem’s numerical solution is based on (full) explicit evolution of the discretized (in-space) variables. Since explicit methods require the time step to be sufficiently small, this condition is very restrictive, particularly for long-time integrations. With the increased computational speed and capacity of today’s multicore computer, it is possible to simulate in detail contaminants’ fate flow using high-performance computing.

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