Rj. Pearson et De. Winterbone, THE SIMULATION OF GAS-DYNAMICS IN ENGINE MANIFOLDS USING NONLINEAR SYMMETRICAL DIFFERENCE-SCHEMES, Proceedings of the Institution of Mechanical Engineers. Part C, Journal of mechanical engineering science, 211(8), 1997, pp. 601-616
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.