三次元移流拡散方程式の，有限要素法による新しい定式化　誤差解析手法によるアプローチ

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  • New Formulation using the Finite Element Method for the Three-Dimensional Convection-Diffusion Equation. Approach using the Error Analysis Technique.
  • 3ジゲン イリュウ カクサン ホウテイシキ ノ ユウゲン ヨウソホウ ニ ヨル

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The unsteady convection-diffusion equation is one of the most important equation in heat and fluid analysis. One of the authors developed the modified Galerkin method (MGM) for the one-dimensional convection-diffusion equation. In this paper, this modified Galerkin method was proposed for three-dimensional convection-diffusion equation using an error analysis technique based on the Fourier series. The correction coefficients of several numerical methods were obtained for various kinds of three-dimensional nodes, and they were used for correcting numerical methods using the implicit and explicit methods. Then all of these methods were investigated from the viewpoints of phase error and dissipation error. The MGM for a regular hexahedra element was proven to be the most efficient numerical method. Through numerical experiments using the implicit and explicit methods, we confirmed the effectiveness of our correction method and the general correspondence between the error analysis and numerical simulation.

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