TVD方法特别适合数值模拟双曲型偏微分方程间断波问题,选用4种典型的TVD格式应用于水击方程的数值模拟。通过水击实例计算,将数值结果与理论解比较,揭示4种不同构造形式的TVD格式在捕捉水击波方面耗散性和压制性数值性能的差异,且TVD格式均优于常规的差分方法;改变计算库朗数条件下的计算结果表明:Harten修正通量TVD格式、TVD-MC格式以及全离散TVD格式在大范围库朗数条件下计算稳定性较差,优选Sweby反扩散TVD格式模拟水击,其计算稳定性良好,精度较高。
Abstract
TVD method is especially suitable for the numerical simulation of discontinuous wave of hyperbolic partial differential equations. In this paper, four typical TVD schemes were presented for the numerical simulation of water hammer equations. Through comparison among example calculation, numerical results and theoretical solutions, the differences in numerical performances in aspects of the dissipative and compressible features of different types of TVD schemes were revealed, and TVD schemes were proved to be superior to conventional difference methods. Calculation results in the presence of varying Courant numbers showed that modified Harten’s TVD scheme, TVDMC scheme and full discrete TVD scheme have poor stability in the presence of a wide range of Courant numbers; whereas optimized Sweby’s TVD scheme for water hammer simulation has good stability and high precision.
关键词
高分辨率 /
TVD格式 /
数值模拟 /
库朗数 /
水击
Key words
high resolution /
TVD scheme /
numerical simulation /
Courant number /
water hammer
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参考文献
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