A Multigrid Method using Explicit Approximate Inverses for the Numerical Solution of Two-Dimensional Time-Dependent Problems

2012 ◽  
Author(s):  
C.K. Filelis-Papadopoulos ◽  
G.A. Gravvanis
Keyword(s):  
Numerical Solution ◽  
Multigrid Method ◽  
Time Dependent ◽  
Two Dimensional ◽  
Approximate Inverses ◽  
Time Dependent Problems

scholarly journals Derivation of boundary conditions for the artificial boundaries associated with the solution of certain time dependent problems by Lax–Wendroff type difference schemes

1982 ◽  
Vol 25 (1) ◽  
pp. 1-18 ◽  
Author(s):  
John C. Wilson
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Time Dependent ◽  
Finite Region ◽  
Partial Differential ◽  
Artificial Boundaries ◽  
Fixed Boundaries ◽  
Time Dependent Problems

Many problems involving the solution of partial differential equations require the solution over a finite region with fixed boundaries on which conditions are prescribed. It is a well known fact that the numerical solution of many such problems requires additional conditions on these boundaries and these conditions must be chosen to ensure stability. This problem has been considered by, amongst others, Kreiss [11, 12, 13], Osher [16, 17], Gustafsson et al. [9] Gottlieb and Tarkel [7] and Burns [1]

scholarly journals Numerical modeling of an avalanche impact against an obstacle with account of snow compressibility

2008 ◽  
Vol 49 ◽  
pp. 27-32 ◽  
Author(s):  
V.S. Kulibaba ◽  
M.E. Eglit
Keyword(s):  
Numerical Modeling ◽  
Equation Of State ◽  
Numerical Solution ◽  
Pressure Distribution ◽  
Time Dependent ◽  
Low Density ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Flow Depth ◽  
Rarefaction Waves

AbstractThe numerical solution to a time-dependent two-dimensional problem of an avalanche impact against a wall is presented. The height of the wall is much larger than the flow depth. Compressibility of the moving snow as well as the effect of gravity is taken into account. Calculations are made for an impact of low-density avalanches with densities <100 kgm–3 obeying the equation of state for a mixture of two gases (air and gas of ice/snow particles). The pressure, density and velocity distributions in the flow as functions of time and space coordinates are calculated, as well as the variation of the flow depth. In particular, the flow height at the wall, the pressure at the wall and the pressure distribution on the slope near the wall are given, demonstrating peaks and falls due to compression shocks and rarefaction waves.

The inviscid transonic flow about a cylinder

1995 ◽  
Vol 301 ◽  
pp. 225-250 ◽  
Author(s):  
Nicola Botta
Keyword(s):  
Mach Number ◽  
Numerical Solution ◽  
Transonic Flow ◽  
Oscillating Solution ◽  
Time Dependent ◽  
Turbulent Regime ◽  
Two Dimensional ◽  
Chaotic Flow ◽  
Regular Flow ◽  
Upwind Method

The two-dimensional inviscid transonic flow about a circular cylinder is investigated. To do this, the Euler equations are integrated numerically with a time-dependent technique. The integration is based on an high-resolution finite volume upwind method.Time scales are introduced and the flow at very short, short and large times is studied. Attention is focused on the behaviour of the numerical solution at large times, after the breakdown of symmetry and the onset of an oscillating solution have occurred. This solution is known to be periodic at Mach number between 0.5 and 0.6.At higher speed, however, a richer behaviour is observed. As the Mach number is increased from 0.6 to 0.98 the numerical solution undergoes two transitions. Through a first one the periodical, regular flow enters a chaotic, turbulent regime. Through the second transition the chaotic flow comes back to an almost stationary state. The flow in the chaotic and in the almost stationary regimes is investigated. A numerical conjecture for the behaviour of the solution at large times is advanced.

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