Symmetric difference schemes, such as the two-step Lax—Wendroff method or MacCormack's method, are used extensively in engine simulation codes in order to achieve second-order accuracy. These schemes, however, produce spurious oscillations when shock waves and contact surfaces are encountered and require the addition of non-linear terms (flux limiters) to cope with such phenomena. The paper reviews briefly the general theory behind the formulation of such nonlinear algorithms and examines the performance of two schemes in particular. The flux corrected transport (FCT) technique has been adopted by several research groups for this purpose and appears to operate satisfactorily for many flows in engine manifolds. It is shown in the present work that, under some circumstances, this method can distort the solution and produce large errors in mass conservation. The symmetric flux limiter due to Davis, based on the total variation diminishing (TVD) criterion, is shown here to avoid such problems and requires similar computational effort to the FCT approach.
