在日中国人CFD研究会講演会

- 第二回講演会
- 講師：肖鋒 東京工業大学総合理工学研究科 助教授
- 講演題目：Computing fluid dynamics by using multi integrated moments
- 開催日：2003年6月28日（土曜日）
- 時 間：午後1:30～
- 開催地：電気通信大学東4号館802
- 講演要旨
Any physical variable or physical field defined in space needs to be represented or measured by one kind or a set of quantities in numerical approximationｓ, for example the value or the gradient of a physical variable at a certain spatial point, the averaged value in respect to a volume or a surface area. We define all of those measures as the moments.

Most conventional numerical methods for time-space variation problems can be classified into either finite difference method (FDM) or finite volume method (FVM). Conceptually, a FDM approximates spatial differential via a consistent differencing by using the values at grid points, while a FVM is usually cast in a formulation that predicts the integrated average value for each mesh cell by examining the net flux across all the cell boundaries. The numerical flux on cell boundary is evaluated then by a consistent approximation based on the cell-integrated average value. The point value in a FDM or the cell-integrated average in a FVM is actually the only quantity memorized and predicted in a numerical model of such a kind. Thus, we call the point value the single 'moment' of the field variable used in FDM, and the cell-integrated average the single 'moment' in FVM. In general, a high order spatial approximation in a conventional FDM or a FVM can be obtained by using extra mesh stencils or by using a compact formulation, the latter usually results in an implicit expression.

Being an alternative to the conventional numerical methods, the CIP (Cubic-Interpolated Pseudoparticle or Constrained Interpolation Profile) scheme makes use of the first order derivatives of the prognostic variable (the gradient) as the extra 'moments' and predicts them in the numerical model as other dependent variables. Employing more than one moment as the dependent variables in its algorithm, the CIP method can be distinguished from the conventional FDM and FVM and classified as the multi-moment method. Analytical and numerical studies show that using multi moments provides more accurate numerical dispersion, more compact computational stencil, more freedoms and flexibilities in constructing numerical models.

Multi-moment as a general concept can, in fact, lead to a new breakthrough for numerical method researches. Being a practice toward such direction, we have developed a new numerical framework for general hydrodynamic simulations by using two integrated moments, namely volume integrated average (VIA) and surface integrated average (SIA). The new framework, which is called VSIAM3 (Volume/Surface Integrated Average based Multi Moment Method) show some new features that are fundamentally different from the traditional ones. For example, the Riemann solver (either the exact one or the approximate one) is not needed in the computations for compressible flows, and a new projection for incompressible fluid can be constructed by using both the VIA and the SIA. The VSIAM3 fluid model has been used for simulating various hydrodynamic problems, most of the numerical outputs are very promising.

The underlying idea of the algorithm and numerical results will be shown in the presentation.