New method for solving the one-dimensional problem of the displacement of petroleum by water taking account of capillary forces

1976 ◽  
Vol 10 (3) ◽  
pp. 434-441
Author(s):  
N. B. Zubov ◽  
G. P. Tsybul'skii
Keyword(s):  
Capillary Forces ◽  
New Method ◽  
Dimensional Problem ◽  
One Dimensional ◽  
The One

The one-dimensional problem of the nonpiston type displacement of a gas by water, taking account of capillary forces

1972 ◽  
Vol 7 (1) ◽  
pp. 62-66
Author(s):  
G. A. Osipova ◽  
G. V. Rassokhin ◽  
G. P. Tsybul'skii
Keyword(s):  
Capillary Forces ◽  
Dimensional Problem ◽  
One Dimensional ◽  
The One

A TWELFTH-ORDER FOUR-STEP FORMULA FOR THE NUMERICAL INTEGRATION OF THE ONE-DIMENSIONAL SCHRÖDINGER EQUATION

2003 ◽  
Vol 14 (08) ◽  
pp. 1087-1105 ◽  
Author(s):  
ZHONGCHENG WANG ◽  
YONGMING DAI
Keyword(s):  
Schrödinger Equation ◽  
Numerical Integration ◽  
Schrodinger Equation ◽  
Numerical Test ◽  
New Method ◽  
Step Method ◽  
One Dimensional ◽  
The Stability ◽  
The One ◽  
Order Four

A new twelfth-order four-step formula containing fourth derivatives for the numerical integration of the one-dimensional Schrödinger equation has been developed. It was found that by adding multi-derivative terms, the stability of a linear multi-step method can be improved and the interval of periodicity of this new method is larger than that of the Numerov's method. The numerical test shows that the new method is superior to the previous lower orders in both accuracy and efficiency and it is specially applied to the problem when an increasing accuracy is requested.

A SIMPLE METHOD TO CONSTRUCT LOCAL EQUILIBRIUM FUNCTION FOR LATTICE BOLTZMANN METHOD

2013 ◽  
Vol 24 (06) ◽  
pp. 1350038
Author(s):  
P. WANG ◽  
S. Q. ZHANG
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Local Equilibrium ◽  
New Method ◽  
Ratio Test ◽  
Simple Method ◽  
One Dimensional ◽  
Equilibrium Function ◽  
The One ◽  
Boltzmann Method

We have developed a simple method to construct local equilibrium function for lattice Boltzmann method (LBM). This new method can make LBM model satisfy compressible flow with a flexible specific-heat ratio. Test cases, including the one-dimensional Sod flow, one-dimensional Lax flow and thermal Couette flow are presented. Good results obtained using proposed new method, indicate that the proposed method is potentially capable of constructing of the local equilibrium function for LBM.

scholarly journals Algorithms for Necklace Maps

2015 ◽  
Vol 25 (01) ◽  
pp. 15-36 ◽  
Author(s):  
Bettina Speckmann ◽  
Kevin Verbeek
Keyword(s):  
Exact Algorithm ◽  
Dimensional Problem ◽  
Order Problem ◽  
Fixed Parameter Tractable ◽  
One Dimensional ◽  
Algorithmic Question ◽  
Fixed Parameter ◽  
Fixed Order ◽  
The One ◽  
Decision Version

Necklace maps visualize quantitative data associated with regions by placing scaled symbols, usually disks, without overlap on a closed curve (the necklace) surrounding the map regions. Each region is projected onto an interval on the necklace that contains its symbol. In this paper we address the algorithmic question how to maximize symbol sizes while keeping symbols disjoint and inside their intervals. For that we reduce the problem to a one-dimensional problem which we solve efficiently. Solutions to the one-dimensional problem provide a very good approximation for the original necklace map problem. We consider two variants: Fixed-Order, where an order for the symbols on the necklace is given, and Any-Order where any symbol order is possible. The Fixed-Order problem can be solved in O(n log n) time. We show that the Any-Order problem is NP-hard for certain types of intervals and give an exact algorithm for the decision version. This algorithm is fixed-parameter tractable in the thickness K of the input. Our algorithm runs in O(n log n + n2K4K) time which can be improved to O(n log n + nK2K) time using a heuristic. We implemented our algorithm and evaluated it experimentally.

Oscillating flames: multiple-scale analysis

2009 ◽  
Vol 465 (2107) ◽  
pp. 2089-2110 ◽  
Author(s):  
Luc Bauwens ◽  
C. Regis L. Bauwens ◽  
Ida Wierzba
Keyword(s):  
Approximate Solution ◽  
Reaction Front ◽  
Burning Velocity ◽  
Propagation Speed ◽  
Multiple Scale ◽  
Expansion Ratio ◽  
Scale Analysis ◽  
Dimensional Problem ◽  
One Dimensional ◽  
The One

A complete multiple-scale solution is constructed for the one-dimensional problem of an oscillating flame in a tube, ignited at a closed end, with the second end open. The flame front moves into the unburnt mixture at a constant burning velocity relative to the mixture ahead, and the heat release is constant. The solution is based upon the assumption that the propagation speed multiplied by the expansion ratio is small compared with the speed of sound. This approximate solution is compared with a numerical solution for the same physical model, assuming a propagation speed of arbitrary magnitude, and the results are close enough to confirm the validity of the approximate solution. Because ignition takes place at the closed end, the effect of thermal expansion is to push the column of fluid in the tube towards the open end. Acoustics set in motion by the impulsive start of the column of fluid play a crucial role in the oscillation. The analytical solution also captures the subsequent interaction between acoustics and the reaction front, the effect of which does not appear to be as significant as that of the impulsive start, however.

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