多種守恆律中央差分法的比較

長久以來，在計算守恆律初始值的數值方法一直都是以採Riemann Solvers的方法為主要的方法，如Godunov方法、ENO方法等，詳情請見[2]。由於近年來所考慮的守恆律問題已日趨複雜，無論是理想氣體、單一的一種氣體，已不是主要的研究對象。而多種氣體混合所構成的問題已漸漸地受到重視。尤其是當混合多種氣體時，其中有一些氣體可以被用來模擬為液體，在各工業技術方面的應用也與日俱增。但是隨著問題越來越複雜，以Riemann Solvers為基礎的方法也越來越難推廣。也隨著方程式數目增多，狀態方程( equation of state )越來越複雜，所以欲建構Riemann Solvers的困難是越來越深了。因此，不需要使用Riemann Solvers的各式中央差分法故越來越被重視。請見[1,2,3,4,5,6]。本論文的目的在比較MUSCL型中央差分法及非交錯網格NT2方法。我們發現這兩者在解析不連續解的能力相當。但MUSCL型中央差分法可使用較大CFL數。

關鍵字

非交錯網格NT2方法； MUSCL型中央差分法； CFL數

並列摘要

Numerical methods adopted to solve hyperbolic conservation laws are mainly Riemann-Solver based methods. Recently, most researchers have focus on mixtures of various types of gases, and the gases considered may have more complex equations of stage. As a result, the Riemann-Solver based methods become significantly harder to construct and implement. For this reason, more and more people are starting to consider whether it is possible to develop central schemes which are free of Riemann-Solvers. The purpose of this thesis is to compare the MUSCL type central and the nonstaggered grid NT2 scheme. It is found that the two schemes have similar capabilities on resolving shocks. However the MUSCL type central scheme can make use of larger CFL number.

並列關鍵字

CFL number. ； MUSCL type central scheme ； nonstaggered grid NT2 scheme

參考文獻

[1] Tien-Yu Sun and Chen-Tzu Hsu A Mulitcomponent Flow Calculation Using MUSCL Type Central Scheme, Department of Mathematics Chung Yuan Christian University, Accepted on September 6, 2000

[2] E.T. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics : a practical introduction, Springer-Verlag, Berlin, 1997

[4] E. Tadmor, Numerical viscosity and the entropy condition for conservative

[5] H. Nessyahu and E. Tadmor, Non-oscillatory central differencing for hyperbolic

[6] G.-S. Jiang and E. Tadmor, Nonoscillatory central schemes for multidimensional

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多種守恆律中央差分法的比較

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