of Mec nical and Intellectual Systems Engineeri , University nf To } , alna , 3190Gofuku , Toyama − shi , T ( 〕yama , 930 呂555 Japan The relaxation equatlons for smoothed particle hydrodynamics ( SPH >are able to suppress the llumerical disorder around the interface ofdifferent 魚 ids. It makes it poss. ible to treat invig . cid multi phase flow without 5eparating it in each 且uid , but the error 〔 〕f them ls not small cnou 彗 h, In thispaper, the error of relaxation equations is discussed for the

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... case of same size particles and the case of differentsize partic 】 es composed of dif「 erent Huids. Formulas to suppress the numerica1 error around 亡 he interface of mult 三phase f ヱ ow are proposed , and methods to determine the smoothing length are discussed, Numerical simulations are carried out for air − water 2 − phase flow to know the effects of these equations and 【methods , Results show that the method to determinethe smoothing length isthe most impertant to suppress the numerical disorder around