CAJ | 학술논문

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。
TVD 방법특별괄합수치모의쌍곡형편미분방정간단파문제，선용4충전형적 TVD 격식응용우수격방정적수치모의。통과수격실례계산，장수치결과여이론해비교，게시4충불동구조형식적 TVD 격식재포착수격파방면모산성화압제성수치성능적차이，차 TVD 격식균우우상규적차분방법；개변계산고랑수조건하적계산결과표명：Harten 수정통량 TVD 격식、TVD-MC 격식이급전리산 TVD 격식재대범위고랑수조건하계산은정성교차，우선Sweby 반확산 TVD 격식모의수격，기계산은정성량호，정도교고。
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.Cal-culation results in the presence of varying Courant numbers showed that modified Harten’s TVD scheme,TVD-MC 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.