Application of the implicit MacCormack scheme to the parabolized Navier-Stokes equations

Lawrence, Scott L.; Tannehill, John C.; Chaussee, D. S.

doi:10.2514/3.8848

Cited by 16 publications

(2 citation statements)

References 16 publications

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“…Moreover, the accuracy of the steady-state solution using MacCormacks hybrid algorithm was comparable to that of the Beam-Warming method for all cases, and was observed to reduce the computing time by a factor of up to three. Lawrence [57] Although not very sophisticated, MacCormack techniques are perfectly satisfactory for many fluid flow applications especially in the case of 2D flows [64]. The MacCormack schemes are particularly adapted for the applications of interest in this dissertation: they are fast and easy to implement, and the accuracy is satisfactory for the type of flow we investigate.…”

Section: Numerical Techniques Developments On Euler Equations Startedmentioning

confidence: 99%

“…The explicit predictor-corrector method which is faster is used over most of computational domain. However, it is not adequate for points in the flow at which the local CFL number exceeds the stability limit [57]: the method adds an implicit procedure to the predictor-corrector sequence.The method is implicit in nature and thus allows a much larger time marching step size.…”

Section: Numerical Techniques Developments On Euler Equations Startedmentioning

confidence: 99%

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Ultrahigh Specific Impulse Nuclear Thermal Propulsion

Charmeau¹,

Cunningham²,

Anghaie³

2009

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PREFACEResearch on nuclear thermal propulsion systems (NTP) have been in forefront of the space nuclear power and propulsion due to their design simplicity and their promise for providing very high thrust at reasonably high specific impulse. During NERVA-ROVER program in late 1950's till early 1970's, the United Sates developed and ground tested about 18 NTP systems without ever deploying them into space. The NERVA-ROVER program included development and testing of NTP systems with very high thrust (~ 250,000 lb f ) and relatively high specific impulse (~ 850 s). High thrust to weight ratio in NTP systems is an indicator of high acceleration that could be achieved with these systems. The specific impulse in the lowest mass propellant, hydrogen, is a function of square root of absolute temperature in the NTP thrust chamber. Therefore, optimizing design performance of NTP systems would require achieving the highest possible hydrogen temperature at reasonably high thrust to weight ratio. High hydrogen exit temperature produces high specific impulse that is a direct measure of propellant usage efficiency.After the cancellation of the US NERVA-ROVER program in early 1970's, the Former Soviet Union continued with the US effort and made improvement in fuel design that enabled design and ground testing of an NTP systems (1984) at temperatures and specific impulses well above what had been achieved during the NERVA-ROVER program (hydrogen exit temperature ~ 3,000 K and specific impulse ~ 1,000 s). The renewed interest in the space nuclear power and propulsion is the main motivation for the proposed research that is intended to develop reactor design and NTP systems for achieving the highest possible specific impulseResearch conducted in support of the development of a new nuclear powered thermal rocket propulsion system is proposed to provide variable thrust in the range of 1,000 to 10,000 lb f of thrust at 1000-1500 seconds of ideal specific impulse (Isp) by heating relatively lowpressure hydrogen propellant to average temperatures ranging from 3000 K to 3250 K. The reactor for the proposed NTR concept is fueled with a uranium tetra-carbide compound that is optimized for resisting atomic and molecular hydrogen at temperatures above 3000 K. Uranium tetra-and tri-carbide fuels feature the highest corrosion resistance properties at elevated temperatures in hydrogen environment. The congruent melting of tetra-and tri-carbides is not overly sensitive to carbon content, as it's the case for uranium bi-carbides such as uraniumzirconium and uranium-niobium carbides. This is a key property of these fuels that would enable their applications for operation at temperatures above 3000 K. The fuel candidate for this concept is the solid solution of uranium-zirconium-niobium-titanium carbide, (U, Zr, Nb, Ti)C.Compare to uranium tri-carbides that have previously been considered for application in NTP systems, the proposed uranium tetra-carbide features higher stability in dissociated hydrogen and more favorable neutronic characteristics...

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Section: Numerical Techniques Developments On Euler Equations Startedmentioning

confidence: 99%

Section: Numerical Techniques Developments On Euler Equations Startedmentioning

confidence: 99%

Ultrahigh Specific Impulse Nuclear Thermal Propulsion

Charmeau¹,

Cunningham²,

Anghaie³

2009

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Numerical solution of the supersonic laminar flow over a two‐dimensional compression corner using an implicit approach

Madhavan

Swaminathan

1986

Numerical Methods in Fluids

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The use of an implicit numerical scheme, analogous to MacCormack's', for the supersonic laminar two-dimensional compression corner flow problem using unsteady Navier-Stokes equations is demonstrated. The technique entails a reduction of about 70 per cent in the computation time for a Courant number of 5, but it is characterized by an increase of approximately 20 per cent in computer memory requirement.

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Numerical Simulation of Compressible Viscous Flows — A Survey —

Peyret

1987

Numerical Simulation of Compressible Navier-Stokes Flows

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Application of the implicit MacCormack scheme to the parabolized Navier-Stokes equations

Cited by 16 publications

References 16 publications

Ultrahigh Specific Impulse Nuclear Thermal Propulsion

Ultrahigh Specific Impulse Nuclear Thermal Propulsion

Numerical solution of the supersonic laminar flow over a two‐dimensional compression corner using an implicit approach

Numerical Simulation of Compressible Viscous Flows — A Survey —

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