A Finite Difference Scheme for Linear Advection Equation Satisfying Three Conservation Laws
A Finite Difference Scheme for Linear Advection Equation Satisfying Three Conservation Laws
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发表时间：
2006
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通讯作者：
Mao De-kang
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作者：
Mao De-kang
针对标量线性平流方程，提出了一种满足三个守恒定律的差分格式，该格式为分段抛物线重构的三阶Godunov型。每个网格中重构函数的系数由三个守恒量决定。虽然该方程是线性的，但所提出的格式是非线性的。数值实验表明，该格式是非线性稳定的，并且在长时间的数值模拟中具有良好的结构保持性。
This paper is concerned with scalar linear advection equation.A difference scheme satisfying three conservation laws is proposed,which is of the third-order Godunov type with piecewise parabolic reconstruction.Coefficients of the reconstructed function in each grid are determined by three conservation quantities.Although the equation is linear,the proposed scheme is nonlinear.Numerical experiments show that the scheme is nonlinearly stable and has good structure-preserving property in long-time numerical simulations.