THE SIMULATION OF GAS-DYNAMICS IN ENGINE MANIFOLDS USING NONLINEAR SYMMETRICAL DIFFERENCE-SCHEMES

Symmetric difference schemes, such as the two-step Lax-Wendroff method or MacCormack's method, are used extensively in engine simulation cod es in order to achieve second-order accuracy. These schemes, however, produce spurious oscillations when shock waves and contact surfaces ar e encountered and require the addition of non-linear terms (flux limit ers) to cope with such phenomena. The paper reviews briefly the genera l theory behind the formulation of such nonlinear algorithms and exami nes the performance of two schemes in particular. The flux corrected t ransport (FCT) technique has been adopted by several research groups f or this purpose and appears to operate satisfactorily for many flows i n engine manifolds. It is shown in the present work that, under some c ircumstances, this method can distort the solution and produce large e rrors in mass conservation. The symmetric flux limiter due to Davis, b ased on the total variation diminishing (TVD) criterion, is shown here to avoid such problems and requires similar computational effort to t he FCT approach.