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<br /> <br />space-step sizes such as OJ, 0.5, and 2.5 cm were <br />tested, It can readily be seen from Figure 8 that the <br />smallest space-step size yields the best results. As the <br />/Sf. size increases, oscillation is magnified and pro- <br />longed, A best.fit line connecting the computed <br />points for each ~ z size can be drawn as marked in <br />broken line (Figure 8). It appears that the best-fit line <br />for lJ;l = 0,] cm merges in the best-fit line for lJ;l = 05 <br />cm which subsequently merges in the best-fit line for <br />!::;z = 2.5 cm and so forth, in essence becoming one <br />single best-fit infiltration decay curve. In other words, <br />if the infIltration rate computation could be reversed, <br />starting at t = 00, a larger ~z could cause the earlier <br />occurrence in oscillation and an eventual breakdown. <br />From the accuracy point of view, it is apparently <br />more accurate to use the smaller ~z in the computa- <br />tion. Despite a large /:,Z used, a divergence problem <br />did not seem to occur on many computer runs tested <br />herein. Because the finite-difference computation <br />with a very smalllY. is time consuming and expensive, <br />use of a small b.z cannot be justified unless one is only <br />interested in the accuracy of the solution. In view of <br />the necessity of considering both accuracy and <br />efficiency involved in a particular computer run, the <br />range of interest associated with the computation of <br />the infIltration rate versus time must be taken into <br />account in the selection of a suitable ~z size. <br /> <br />Figure 8 demonstrates the differences in the <br />range of the computed infiltration rate for the three <br />different /:,Z sizes used in the computation, given the <br />various lengths of computer time (e.g" UNIVAC <br />I 108 CPU time 95 seconds for /:,Z = 0.1 em up to t = <br />0.02 hours, 155 seconds for lJ;l = 05 cm up to t = 0,8 <br />hours, and 64 seconds for /:,Z = 2,5 cm up to t = 10 <br />hours), Computer output for each /:,Z size used is <br /> <br />It <br />I <br />s <br />" . <br />.. <br />l' <br />~ z <br />~ <br />, <br />n <br />;! <br />.. 5 <br />~ ~ <br />:s <br /> <br />labeled in different symbols, An inspection of Figure <br />8 reveals that using a lJ;l size of either 0.1,0,5, or 25 <br />em could yield approximately the same inftltration <br />decay curve at about half an hour after ponding. <br />However, in terms of computer time involved in the <br />computation, use of lJ;l = 2,5 em would be more than <br />twenty times less expensive than that of lJ;l = 05 em <br />as far as that range of the infiltration rate (Le., t>O,5 <br />hours) is concerned. In another case, if one is <br />interested in the infiltration rate shortly after pond- <br />ing, say t<0.002 hours (or 7.2 seconds), a/:,z size of <br />0.1 em or less shouid be used. Use of a /:,z size of 0.5 <br />or 2.5 cm in the latter case is obviously not adequate. <br /> <br />Effect of initial moisture content (00) <br /> <br />Different initial moisture contents were tested <br />to determine the effect of initial moisture content on <br />the accuracy of the present finite-difference modeL <br />For comparison, an equal ~z size, 2.5 cm, was used <br />and values of all variables except 80 were kept <br />constant in the computation of the same hypothetical <br />conditions shown in Figure 8. Computed inftltration <br />decay curves for 00 equal to 0.1,0.2,03, and 0.4, by <br />using about the equal length of computer time were <br />depicted in different symbols, as shown in Figure 9, <br />As anticipated, the higher the initial moisture con- <br />tent, the smaller the computational oscillation When <br />the initial moisture content is high such as 0.4, close <br />to saturation, the infIltration rate computed by <br />means of Eq, 33 does not appear to have a large error <br />for t>OJ hours, As the value of 00 decreases, <br />computational oscillation, although damped out in <br />the end, is amplified and prolonged, The present <br />finite-difference model, was tested and shown to be <br />valid up to 00 = om, but it broke down for 00 less <br /> <br /> <br />z <br /> <br />a%.:: 0.1 em <br />- a%.:: 0.5 em <br />.....:lo- az:: 2.5 em <br /> <br />_______ _ __ _ ____ _ _ f_K!...:.~~:.m~~ __ __ _ _ ___ __ ___~________ <br /> <br />3 4 S6789 <br />I <br /> <br />z <br /> <br />3 4 56789 <br />'A <br /> <br />10-4 <br /> <br />z <br /> <br />3 4 56789 , <br />10' <br /> <br />, <br /> <br />3 4 5 6789 <br />10-2 <br /> <br />z <br /> <br />3 4 56789 <br />10.1 <br /> <br />z <br /> <br />Figure 8, Examples of the effect of space-step (Az) size on computed infdtration rate (f) under a hypothetical <br />immediate ponding situation, <br /> <br />Time - t - hour <br /> <br />26 <br />