scholarly journals NUMERICAL SOLUTION OF THE TWO-DIMENSIONAL TIME-DEPENDENT MULTIGROUP EQUATIONS.

1969 ◽  
Author(s):  
W. McCormick, Jr. ◽  
K. Hansen
Keyword(s):  
Numerical Solution ◽  
Time Dependent ◽  
Two Dimensional

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.

B-Spline Gaussian Collocation Software for Two-Dimensional Parabolic PDEs

2013 ◽  
Vol 5 (04) ◽  
pp. 528-547 ◽  
Author(s):  
Zhi Li ◽  
Paul Muir
Keyword(s):  
Numerical Solution ◽  
Differential Algebraic Equations ◽  
Time Dependent ◽  
Parabolic Partial Differential Equations ◽  
Test Problems ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Parabolic Pdes ◽  
Spline Basis ◽  
Gauss Points

AbstractIn this paper we describe newB-spline Gaussian collocation software for solving two-dimensional parabolic partial differential equations (PDEs) defined over a rectangular region. The numerical solution is represented as a bi-variate piecewise polynomial (using a tensor productB-spline basis) with time-dependent unknown coefficients. These coefficients are determined by imposing collocation conditions: the numerical solution is required to satisfy the PDE and boundary conditions at images of the Gauss points mapped onto certain subregions of the spatial domain. This leads to a large system of time-dependent differential algebraic equations (DAEs) which is solved using the DAE solver, DASPK. We provide numerical results in which we use the new software, called BACOL2D, to solve three test problems.

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