On a class of center-typed third order difference scheme orienting to engineering utilizations

Techniques are developed for the construction of difference schemes by analyzing their dissipation relations and using relinearizing process; A centertyped third order nonlinear scheme is presented, which has the equivalent grid stencil as the NND scheme. Because the linear part of the scheme has well performance about the dissipative characteristics, and the linear form of it will be preferred as far as possible due to the relinearizing technique, the improvement will be obtained theoretically on the resolution and maitainance ability about the vortices in computations; On the other hand, the scheme will change back into NNDlike scheme by the nonlinear procedure when encoutnering nonsmooth region, and the dissipation and stability mechanism will be brought into action. The validating computations show that, the scheme can be used in computations containing vortices and perturbations with viscosity, and the simple form of the algorithm makes it easily utilized in engineering purpose and extended to finite volume method.