Discrete mechanics is presented as an alternative to the equations of fluid mechanics, in particular to the Navier-Stokes equation. The derivation of the discrete equation of motion is built from the intuitions of Galileo, the principles of Galilean equivalence and relativity. Other more recent concepts such as the equivalence between mass and energy and the Helmholtz-Hodge decomposition complete the formal framework used to write a fundamental law of motion such as the conservation of accelerations, the intrinsic acceleration of the material medium, and the sum of the accelerations applied to it. The two scalar and vector potentials of the acceleration resulting from the decomposition into two contributions, to curl-free and to divergence-free, represent the energies per unit of mass of compression and shear.

The solutions obtained by the incompressible Navier-Stokes equation and the discrete equation of motion are the same, with constant physical properties. This new formulation of the equation of motion makes it possible to significantly modify the treatment of surface discontinuities, thanks to the intrinsic properties established from the outset for a discrete geometrical description directly linked to the decomposition of acceleration. The treatment of the jump conditions of density, viscosity and capillary pressure is explained in order to understand the two-phase flows. The choice of the examples retained, mainly of the exact solutions of the continuous equations, serves to show that the treatment of the conditions of jumps does not affect the precision of the method of resolution.

离散力学是流体力学方程的替代方案，特别是Navier-Stokes方程。离散运动方程的推导是根据伽利略的直觉，伽利略等价原理和相对论建立的。其他较新的概念（例如质量与能量的等效性和Helmholtz-Hodge分解）完善了用于编写运动基本定律的形式框架，例如运动的守恒性，物质介质的固有加速度以及运动的总和。应用于它的加速度。分解为两个分量（无卷曲和无散度）的加速度产生的两个标量和矢量势，代表每单位质量的压缩和剪切能量。

由不可压缩的Navier-Stokes方程和运动的离散方程获得的解是相同的，具有恒定的物理属性。由于从一开始就建立了直接与加速度分解相关的离散几何描述的固有特性，因此运动方程的这种新公式形式可以显着修改表面不连续性的处理。解释了密度，粘度和毛细压力跳跃条件的处理，以了解两相流。保留示例的选择，主要是连续方程的精确解，可以表明对跳跃条件的处理不会影响解析方法的精度。