Incompressibility is a fundamental condition in most fluid models. Accumulation of simulation errors violates it and causes volume loss. Past work suggested correction methods to battle it. These methods, however, are imperfect and in some cases inadequate. We present a method for fluid simulation that strictly enforces incompressibility based on a grid-related definition of discrete incompressibility. We formulate a linear programming (LP) problem that bounds the number of particles that end up in each grid cell. A variant of the band method is offered for acceleration, which requires special constraints to ensure volume preservation. Further acceleration is achieved by simplifying the problem and adding a special band correction step that is formulated as a minimum-cost flow problem (MCFP). We also address coupling with solids in our framework and demonstrate advantages over prior work.

翻译：不可压缩性是大多数流体模型中的基本条件。模拟误差的积累会破坏该条件并导致体积损失。先前的研究提出了修正方法来解决这一问题，但这些方法存在不完善之处，在某些情况下并不充分。我们提出了一种流体模拟方法，该方法基于网格相关的离散不可压缩性定义，严格强制执行不可压缩性。我们构建了一个线性规划（LP）问题，用于限制每个网格单元中最终存在的粒子数量。为加速计算，我们引入了带宽方法的变体，该方法需要特殊的约束条件以确保体积守恒。通过简化问题并引入一个特殊的带宽修正步骤（该步骤被表述为最小成本流问题（MCFP）），进一步实现了加速。我们还处理了框架中与固体的耦合，并展示了相较于先前工作的优势。