Higher‐order explicit schemes based on the method of characteristics for hyperbolic equations with crossing straight‐line characteristics

2021 ◽  
Author(s):  
Taras I. Lakoba ◽  
Jeffrey S. Jewell
Keyword(s):  
Method Of Characteristics ◽  
Hyperbolic Equations ◽  
Higher Order ◽  
Explicit Schemes ◽  
The Method Of Characteristics ◽  
Straight Line

Solution of Impact-Induced Flexural Waves in a Circular Ring by the Method of Characteristics

1998 ◽  
Vol 65 (3) ◽  
pp. 569-579 ◽  
Author(s):  
V. P. W. Shim ◽  
S. E. Quah
Keyword(s):  
Numerical Scheme ◽  
Method Of Characteristics ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Circular Ring ◽  
Higher Order ◽  
Flexural Waves ◽  
The Method Of Characteristics ◽  
Finite Difference Equations ◽  
Generalized Displacements

A study of elastic wave propagation in a curved beam (circular ring) is presented. The governing equations of motion are formulated in two forms based on Timoshenko beam theory. Solutions are obtained using the method of characteristics, whereby a numerical scheme employing higher-order interpolation is proposed for the finite difference equations. Results obtained are verified by experiments; it is found that use of the higher-order numerical scheme improves correlation with experimental results. Comparison of the relative accuracy between the two mathematical formulations—one in terms of generalized forces and velocities and the other in terms of generalized displacements—shows the former to be mathematically simpler and to yield more accurate results.

scholarly journals An investigation, by the method of characteristics, of the lateral expansion of the gases behind a detonating slab of explosive

1947 ◽  
Vol 191 (1027) ◽  
pp. 524-541 ◽  
Keyword(s):  
Shock Waves ◽  
Method Of Characteristics ◽  
Hyperbolic Equations ◽  
Surrounding Medium ◽  
Graphical Form ◽  
Gas Field ◽  
Fluid Medium ◽  
Gaseous Products ◽  
The Method Of Characteristics ◽  
Set Up

The phenomena occurring when an uncased explosive charge is detonated in a fluid medium are examined by hydrodynamical methods. Attention is focused chiefly on the pressure and velocity distributions in the gaseous products of the explosion, which expand laterally behind the detonation wave as it travels down the charge, the results being shown in graphical form. To simplify the problem, the charge, and the gas and fluid fields, were treated as two-dimensional. The hydrodynamical equations were solved numerically using the method of characteristics. This dates back to Monge, but it is only recently that it has been applied to the numerical solution of hyperbolic equations. The methods of numerical integration used in this paper are similar to those developed early in the war by the Research Section of the External Ballistics Department, Ordnance Board, for determining the velocity distributions around projectiles moving at supersonic speeds. The nature of the boundary conditions made it necessary to find explicit theoretical formulae for the gas field near the charge, and the analysis involved is given at length. For the problem in which the surrounding medium is air, the shape and position of the shock waves set up by the explosion are calculated. The shock waves are found to be straight to the nominal accuracy of the calculations (1 in 5000) for six charge widths from their intersections with the block of explosive.

Non-symmetric flow in Laval type nozzles

1972 ◽  
Vol 273 (1232) ◽  
pp. 185-235 ◽  
Keyword(s):  
Steady State ◽  
Combustion Chamber ◽  
Method Of Characteristics ◽  
Three Dimensions ◽  
Symmetric Flow ◽  
Gaseous Flow ◽  
The Method Of Characteristics ◽  
Lateral Forces

The equations of the steady state, compressible inviscid gaseous flow are linearized in a form suitable for application to nozzles of the Laval type. The procedure in the supersonic phase is verified by comparing solutions so obtained with those derived by the method of characteristics in two and three dimensions. Likewise, the solutions in the transonic phase are com pared with those obtained by other investigators. The linearized equation is then used to investigate the nat re of non-symmetric flow in rocket nozzles. It is found that if the flow from the combustion chamber into the nozzle is non-symmetric, the magnitude and direction of the turning couple produced by the emergent jet is dependent on the profile of the nozzle and it is possible to design profiles such that the turning couples or lateral forces are zero. The optimum nozzle so designed is independent of the pressure and also of the magnitude of the non-symmetry of the entry flow. The formulae by which they are obtained have been checked by extensive static and projection tests with simulated rocket test vehicles which are described in this paper.

Boundary Layer Closure and Heat Transfer in Constant Base Pressure and Simple Wave Guns

1978 ◽  
Vol 100 (4) ◽  
pp. 690-696 ◽  
Author(s):  
A. D. Anderson ◽  
T. J. Dahm
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Method Of Characteristics ◽  
Simple Wave ◽  
Momentum Equation ◽  
Base Pressure ◽  
Two Dimensional ◽  
The Method Of Characteristics

Solutions of the two-dimensional, unsteady integral momentum equation are obtained via the method of characteristics for two limiting modes of light gas launcher operation, the “constant base pressure gun” and the “simple wave gun”. Example predictions of boundary layer thickness and heat transfer are presented for a particular 1 in. hydrogen gun operated in each of these modes. Results for the constant base pressure gun are also presented in an approximate, more general form.

scholarly journals Numerical Boundary Conditions for Solar Magnetic Hydrodynamic Flows Using the Method of Characteristics

1996 ◽  
Vol 154 ◽  
pp. 149-153
Author(s):  
S. T. Wu ◽  
A. H. Wang ◽  
W. P. Guo
Keyword(s):  
Boundary Conditions ◽  
Method Of Characteristics ◽  
Numerical Solutions ◽  
The Self ◽  
Time Dependent ◽  
Solar Plasma ◽  
The Method Of Characteristics ◽  
Mhd Simulations ◽  
Self Consistent ◽  
Dynamic Structures

AbstractWe discuss the self-consistent time-dependent numerical boundary conditions on the basis of theory of characteristics for magnetohydrodynamics (MHD) simulations of solar plasma flows. The importance of using self-consistent boundary conditions is demonstrated by using an example of modeling coronal dynamic structures. This example demonstrates that the self-consistent boundary conditions assure the correctness of the numerical solutions. Otherwise, erroneous numerical solutions will appear.

Sign in / Sign up

Export Citation Format

Share Document