Overview of Mathematical and Numerical Solution Methods

2020 ◽  
pp. 35-56
Author(s):  
Dirk Scheer ◽  
Holger Class ◽  
Bernd Flemisch
Keyword(s):  
Numerical Solution ◽  
Numerical Solution Methods ◽  
Solution Methods

Modelling and Simulation of the Melting Process in Electric Arc Furnaces-Influence of Numerical Solution Methods

2015 ◽  
Vol 87 (5) ◽  
pp. 581-588 ◽  
Author(s):  
Thomas Meier ◽  
Vito Logar ◽  
Thomas Echterhof ◽  
Igor Škrjanc ◽  
Herbert Pfeifer
Keyword(s):  
Numerical Solution ◽  
Melting Process ◽  
Electric Arc ◽  
Modelling And Simulation ◽  
Electric Arc Furnaces ◽  
Arc Furnaces ◽  
Numerical Solution Methods ◽  
Solution Methods

Numerical Solution of Solid Propellant Transient Combustion

1979 ◽  
Vol 101 (2) ◽  
pp. 359-364 ◽  
Author(s):  
D. E. Kooker ◽  
C. W. Nelson
Keyword(s):  
Numerical Solution ◽  
Burning Rate ◽  
Solid Propellant ◽  
External Pressure ◽  
Finite Amplitude ◽  
Stable Model ◽  
Final State ◽  
Numerical Predictions ◽  
Numerical Solution Methods ◽  
Solution Methods

Three thermal theories of solid propellant combustion, [1, 2, 3], all based on the quasi-steady flame assumption, were subjected to a rapidly rising external pressure field simulating a gun combustion chamber. Transient burning rates were computed by four different numerical solution methods; the best results were obtained with an invariant imbedding scheme. The numerical predictions show that (1) burning rate “runaway” is a numerical difficulty and is not a solution to the models, (2) the final state of an intrinsically unstable model at constant pressure is composed of repeating finite-amplitude spikes, and (3) the dynamic burning rate from a linearly-stable model can be many times greater than r = apn.

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