中文摘要：

为高效求解扩展型Boussinesq水波方程，建立了基于有限差分和有限体积方法的混合数值格式。将一维控制方程写为守恒形式，方程中通量部分采用有限体积方法求解，剩余部分采用有限差分方法求解。其中，有限体积方法采用Godunov类高分辨率格式，并结合HLL（Harten—LaxandvanLeer）式黎曼问题近似解求界面数值通量，黎曼问题界面左右变量通过高精度状态插值方法（MUSCL）构筑。有限差分方法则采用具有二阶精度的中心差分公式进行。采用具有TVD（TotalVariationDiminishing）性质的三阶龙格-库塔多步积分法进行时间积分。对数值模式进行了验证，数值结果同解析解或实验数据吻合良好。

英文摘要：

To efficiently solve the extended Boussinesq equations, a hybrid finite-difference and finite-volume scheme is developed. The one-dimensional governing equations are kept in conservation form. The flux term is diseretized using the finite volume method, while the remaining terms are discretized using the finite difference method. A Godunov-type high resolution scheme, in conjunction with the Harten-Lax and van Leer （HLL） Riemann solver and the higher accura- cy MUSCL （Monotone Upwind Schemes for Scalar Conservation Laws） method for variable reconstruction, is adopted to compute the interface flux. High order central difference formulas are used to discretize the remaining terms. The third order Runge-Kutta method with total variation diminishing tests are conducted for model validation, and the computed （TVD） property is adopted for time marching. Numerical results agree well with experimental data.