A WENO scheme without implementing the flux-splitting procedure is developed in the present paper. The scheme is deduced by taking the optimized coefficients, originally constant in any flux-splitting WENO scheme, to ...A WENO scheme without implementing the flux-splitting procedure is developed in the present paper. The scheme is deduced by taking the optimized coefficients, originally constant in any flux-splitting WENO scheme, to vary with respect to eigenvalues in the characteristic space. As a result, the weights are associated with both the eigenvalues and the smoothness measurements. The scheme is formulated to avoid the implementing of the flux-splitting procedure via computation of the weighs of WENO stencils, and is capable of reducing the numerical dissipation. Numerical experiments show that the new scheme is less dissipative than the WENO scheme with flux-splitting, and possesses higher resolution using the same grid mesh. Computations of the test cases also demonstrate a comparatively higher computational efficiency of the new scheme. Especially, for problems involving shocks, strong shear and long time evolution, the solutions computed by the presently developed scheme with no flux-splitting and the other existing methods with flux-splitting differ remarkably from each other, and the new scheme is proven to be an effective way for controlling the numerical dissipation and retaining the real effects of the physical viscosity.展开更多
文摘A WENO scheme without implementing the flux-splitting procedure is developed in the present paper. The scheme is deduced by taking the optimized coefficients, originally constant in any flux-splitting WENO scheme, to vary with respect to eigenvalues in the characteristic space. As a result, the weights are associated with both the eigenvalues and the smoothness measurements. The scheme is formulated to avoid the implementing of the flux-splitting procedure via computation of the weighs of WENO stencils, and is capable of reducing the numerical dissipation. Numerical experiments show that the new scheme is less dissipative than the WENO scheme with flux-splitting, and possesses higher resolution using the same grid mesh. Computations of the test cases also demonstrate a comparatively higher computational efficiency of the new scheme. Especially, for problems involving shocks, strong shear and long time evolution, the solutions computed by the presently developed scheme with no flux-splitting and the other existing methods with flux-splitting differ remarkably from each other, and the new scheme is proven to be an effective way for controlling the numerical dissipation and retaining the real effects of the physical viscosity.
