Added Mass

Added mass (also known as virtual mass) is an effect resisting the acceleration of a dynamic rigid body inside a fluid. When a body changes its velocity, it also moves some volume of the fluid that surrounds it. Due to the surrounding fluid, the acceleration of the body is affected, and will be slower. Afterward, the fluid around the rigid body accelerates and moves according to the rigid body motion. Then, when the rigid body tends to slow down, the velocity of the surrounding fluid makes the deceleration slower.

The added mass can be considered as a force related to the object's acceleration relative to the surrounding fluid. Simulating the added mass by applying forces tends to be a source of instability, unless high simulation frequencies or higher order integrators are used (which is usually not the case in an interactive simulation setting). The body acceleration has an effect on the forces generated by the added mass, and the forces applied on the body have a direct effect on its acceleration. For this reason we use a different approach to simulate the added mass: the tensor K. It is represented by a 6x6 matrix. The tensor is the sum of the mass-inertia tensor KB and the added mass tensor KF:

where:

and:

The added mass tensor KF can be used to simulate a dynamic rigid body in a fluid, and has the following form:

The sub-matrix L represents the coupling between linear motions, the sub-matrix A couples angular motion, and the sub-matrix P couples the angular motion with the linear motion. Note that KF is symmetrical, as are L and A, but not P.

Note
The added-mass tensor KF has to be provided by the user. The user must know how to compute this tensor to simulate the effect of the added mass. See Configuring the Added Mass.

The physics pipeline in Vortex® is capable of managing the full 6x6 mass matrix K (defined above) in the equation of motion. The mass matrix is used to compute the acceleration from forces, and to solve the various constraints. Due to the inclusion of KF in K, the fluid effects upon the rigid body are accounted for in the simulation.