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By C.R. Scott

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There are two ways of studying the convection of a variable distribution. Ignoring diffusional influences (conduction in the case of heat), we can assign our variable values to particles. " We could in this way reconstruct the distribution at various time increments from some initially known distribution if the velocities were somehow known. , consider a given distribution of w (known everywhere) and then discretize this information to a fixed space and at time t = 0, letting the w values be the average over a grid interval.

What we need for more rapid convergence is a form that will allow us larger a's without causing instability. In other words, we can sacrifice the accuracy sought in the heat equation to produce the overshoot effect that will give more rapid convergence. The final converged solution is our main interest rather than the value of a single iterate or time step as is true in the heat equation. 14) Note that for a = 2, r is equal to -1 independent of kLlx and that all values for a < 2 are stable. Overshoot can be regulated so that short waves will overshoot optimally for rapid convergence.

The tear will be rehealed if fluid feeding from the main bath to the torn region can readily occur. , increases with rate of cooling and sharpness of a corner in a casting. Both the strength of the solid shell and the probability of tear rehealing will decrease as the freezing range of the alloy increases. Thus the frequency of hot tear defects will increase as the rate of chilling increases and as the freezing range of the alloy increases. Below, the outlines of a systems analysis of the hot tearing defect is presented.

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