Study On Riemann Solutions Of Non-isentropic Euler Equations And Chromatography Equations

This thesis study the limit of Riemann solutions behaviors,at first,for the nonisen-tropic Euler equations of Chaplygin gas,and analyse and prove that when the pressure disappears,there will be ? shock or vacuum state formation in Riemann solutions Then we construct the Riemann solutions of nonsimplified chromatographic equations and analyse all kinds of the interaction between waves,we find when the difference between different initial values tend to(-1)+,there will be zero wavesFirstly,we study the limit behaviors of the Riemann solutions of Chaplygin gas nonisentropic Euler equations.When u->u+,and the parameter ? tends to a centain value,will form ? shock wave.Different from isentropic fluid,the weight of ? shock wave is determined by density p and internal energy H.At the same time,we deduce the entropy inequality and use the entropy inequality,the uniqueness of ? shock wave is obtained.If u-<u+,cavitation occurs when the parameter ? approaches 0Secondly,we study the Riemann problem of two pieces of initial value nonsimplified chromatographic equations.Through the analysis of phase plane,we establish the Riemann solutions of the nonsimplified chromatographic equations.When the difference between negative state approaches(-1)+,there are zero shock and zero ? shock.When the difference between positive state tends to(-1)+,there are zero rarefaction waves Then we study the initial value of three constant states,through the analysis of wave interaction,it is found that when the difference between negative state approaches(-1)+,zero shock and zero ? shock will be generated.When the difference between intermediate state approaches(-1)+,zero rarefaction wave will be generatedFinally,numerical simulation is used to verify our conclusions.