By Biringen S., Chow C.-Y.
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Extra resources for An Introduction to Computational Methods in Fluids
35 in Fig. 91 s. For a take-off speed of 67 m/s, this is the approximate configuration of the three-dimensional trailing vortex sheet at a distance of 128 m behind the airplane. The plot also shows that after the sheet has been rolled up, the centers of the two spirals are separated by a distance shorter than the wing span b. 5 also reveals that the tip region of the vortex sheet descends slower than the middle region. The vertical position of the midpoint of the sheet descends initially with speed 0 2a, and slows down toward a constant speed approximately equal to half of that value.
4 according to a constant time increment; therefore, the range is not specifically shown in the output. Furthermore, an algorithm has to be found so that the maximum of a function can be located automatically by the computer. The range can be found approximately by using Fig. 2. Suppose that in the numerical integration the point Q is the first computed point at which the body falls back on or below the horizon. Tracing back to the previous time step, the body was at the point P. The path connecting P and Q is, in general, a curve, but can be approximated by a straight line if the time interval is small.
2U sin ωT. Hint Since the density of copper is much higher than that of air, the buoyancy and added mass can be neglected in the equations of motion. It can be shown that the component of viscous force in the direction of v is 1 2 ρf dcd (u cos θ − v) (u sin θ )2 + (u cos θ − v)2 where θ and v are indicated in Fig. 1. The direction of this force component is controlled by the sign of (u cos θ − v). 4 FOURTH-ORDER RUNGE-KUTTA METHOD FOR COMPUTING TWO-DIMENSIONAL MOTIONS OF A BODY THROUGH A FLUID Consider the translation motion of a body through a fluid in the x -y plane, where y is in the direction opposite to that of the gravitational acceleration, as sketched in Fig.
An Introduction to Computational Methods in Fluids by Biringen S., Chow C.-Y.