Characteristics of the general equations of gas dynamics

Rusanov, V. V.

doi:10.1016/0041-5553(63)90294-5

Cited by 22 publications

(17 citation statements)

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“…The Monge cone d 2 N À 1. A mathematical analysis, [3,16], enables to determine the type and the number of compatibility conditions to be used. This is resumed in the Table 1.…”

Section: Compatibility Conditions In the 3d Physical Spacementioning

confidence: 99%

A multi-dimensional time-marching method of characteristics for viscous and heat-conducting flows

Ballmann

Sanaknaki

2000

Archive of Applied Mechanics (Ingenieur Archiv)

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A numerical scheme is presented which employs the characteristic surfaces in space-time for solving Navier-Stokes equations for compressible¯uid¯ow. We consider the general case of a three-dimensional¯ow, a simpli®cation of which yields the equations of the two-dimensional case. Emphasis is put on the method itself. We apply it to simulate a laminar hypersonic¯ow around a circular cylinder of a ®ve-components gas mixture of nitrogen and oxygen with thermally perfect constituents and at chemical nonequilibrium. First, the partial differential equations are transformed into a standard form with directional derivatives, enabling to attain the compatibility conditions, including the viscosity terms. These conditions are discretized by approximating their integrals along the corresponding characteristic surfaces. The result is an explicit time-marching numerical scheme. Using a grid ®tted between the shock and the cylinder, and starting from roughly estimated initial conditions, a steady solution is searched. A comparison is made with the solution obtained under the assumption of a perfect gas.

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“…The Monge cone d 2 N À 1. A mathematical analysis, [3,16], enables to determine the type and the number of compatibility conditions to be used. This is resumed in the Table 1.…”

Section: Compatibility Conditions In the 3d Physical Spacementioning

confidence: 99%

A multi-dimensional time-marching method of characteristics for viscous and heat-conducting flows

Ballmann

Sanaknaki

2000

Archive of Applied Mechanics (Ingenieur Archiv)

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“…For more details see Ref. 3. In the reference plane characteristic theory, 1 the original continuity, x-momentum, ^-momentum, and energy equations can be written as four compatibility equations on three characteristics.…”

Section: Boundary Conditionsmentioning

confidence: 99%

Stability aspects of diverging subsonic flow

Cline

1980

AIAA Journal

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“…A method developed in the 1960s, explained in detail by 15 Rusanov (Rusanov, 1963). MOC is applied to reduce hyperbolic partial differential equations, such as the SSWE, to a family of ordinary differential equations.…”

Section: Methods Of Characteristics For Sswementioning

confidence: 99%

Tree-based mesh-refinement GPU accelerated tsunami simulator for real time operation

Acuna¹,

Aoki²

2017

Preprint

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Abstract. This paper presents a fast and accurate tsunami real time operational model to compute across-ocean wide-simulations completely on GPU. The spherical shallow water equations are solved using the method of characteristics and upwind cubic-interpolation, to provide high accuracy and stability. A customized, user interactive, tree based mesh 10 refinement method is implemented based on distance from the coast and focal areas to generate a memory efficient domain with resolutions of up to 50m. Three GPU kernels, specialized and optimized (wet, wall and inundation) are developed to compute the domain block mesh. Multi-GPU is used to further speed up the computation and a weighted Hilbert space filling curve is used to produce balanced work load. Hindcasting of the 2004 Indonesia tsunami is presented to validate and compare the agreement of the arrival times and main peaks at several gauges. Inundation maps are also produced for Kamala 15 and Hambantota to validate the accuracy of our model. Test runs on three Tesla P100 cards on Tsubame 3.0 could fully simulate 10 hours in just under 10 minutes wall clock time.

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Characteristics of the general equations of gas dynamics

Cited by 22 publications

References 0 publications

A multi-dimensional time-marching method of characteristics for viscous and heat-conducting flows

A multi-dimensional time-marching method of characteristics for viscous and heat-conducting flows

Stability aspects of diverging subsonic flow

Tree-based mesh-refinement GPU accelerated tsunami simulator for real time operation

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