CAJ | 학술논문

基于一维阻尼潮波传播方程解析解,从求解数值格式及Heuristic稳定性分析方面,讨论了数值解的精度、计算耗时和摩阻系数选取等问题.研究结果表明:1)Courant数小于1时,潮波方程显格式解的精度略高于隐格式解,计算耗时少于隐格式解;2)为减少计算耗时,潮波方程的隐格式解允许较大的时间步长,但解的精度有所降低,须通过减小底床摩阻系数以保证计算精度;3)隐格式解摩阻系数的选取与Courant数有关,Courant数越大,摩阻系数的选取值比实际值越小,通过理论分析结合数值试验得到了相应的关系式.这些研究结论对实际海域的潮波传播的数值模拟具有重要的应用价值.
기우일유조니조파전파방정해석해,종구해수치격식급Heuristic은정성분석방면,토론료수치해적정도、계산모시화마조계수선취등문제.연구결과표명:1)Courant수소우1시,조파방정현격식해적정도략고우은격식해,계산모시소우은격식해;2)위감소계산모시,조파방정적은격식해윤허교대적시간보장,단해적정도유소강저,수통과감소저상마조계수이보증계산정도;3)은격식해마조계수적선취여Courant수유관,Courant수월대,마조계수적선취치비실제치월소,통과이론분석결합수치시험득도료상응적관계식.저사연구결론대실제해역적조파전파적수치모의구유중요적응용개치.
Based on the analytical solution of one-dimensional propagating equation of dam ping tidal wave, the precision of numerical solution, computational time and determining of friction factor are discussed considering the numerical schemes of equation and the Heuristic stability analysis in this paper. The results show that (1) when Courant number is less than 1, the explicit solution of tidal wave equation has higher precision and requires less computational time than the implic it solution;(2) large time step is allowed in implicit scheme in order to reduce the computational time, but the precision of solution also reduces and the calculation precision should be guaranteed by reducing bottom friction factor;(3) determining of friction factor in implicit solution is related to Courant number, and the determined friction factor is smaller than the natural value when Courant number is larger,and their relationship formula is given from the theoretical analysis and the numerical experiments. These results have important application value for the numerical simulation of the tidal wave propagating process in the natural seawaters.