The effect of the formulation of nonlinear terms on aliasing errors in spectral methods. (English) Zbl 0858.76060
Summary: The effect on aliasing errors of the formulation of nonlinear terms, such as the convective terms in the Navier-Stokes equations of fluid dynamics, is examined. A Fourier analysis shows that the skew-symmetric form of the convective term results in a reduced amplitude of the aliasing errors relative to the conservative and nonconservative forms. The three formulations of the convective term are tested for Burger’s equation and in large-eddy simulations of decaying compressible isotropic turbulence. The results for Burgers’ equation show that, while in certain cases the nonconservative form has the lowest error, the skew-symmetric form is the most robust. For the turbulence simulations, the skew-symmetric form gives the most accurate results, consistent with the error analysis.
MSC:
| 76M25 | Other numerical methods (fluid mechanics) (MSC2010) |
| 76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |
| 65N35 | Spectral, collocation and related methods for boundary value problems involving PDEs |
Keywords:
skew-symmetric form of convective term; Navier-Stokes equations; Fourier analysis; Burger’s equation; large-eddy simulations; decaying compressible isotropic turbulenceReferences:
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