1/21/2024 0 Comments Fluid simulation games![]() To define the equations of motion in a particular context, it is also necessary to specify boundary conditions (that is, how the fluid behaves near solid obstacles or other fluids). Where p is the pressure, is the mass density, f represents any external forces (such as gravity), and is the differential operator: Subject to the incompressibility constraint: ![]() Given these assumptions, the velocity can be described by the momentum equation: In computer animation, fluid is commonly modeled as inviscid (that is, more like water than oil) and incompressible (meaning that volume does not change over time). The motion of a fluid is often expressed in terms of its local velocity u as a function of position and time. (Note that superscripts are used to index the time step and do not imply exponentiation.) Be warned, however, that the forward Euler scheme is not a good choice numerically-we are suggesting it only as a way to think about the equations. In other words, the value of x at the next time step equals the current value of x plus the current rate of change f ( x n, t n ) times the duration of the time step t. The reader may find it easier to think about this relationship in the discrete setting of forward Euler integration: Which says that the rate at which some quantity x is changing is given by some function f, which may itself depend on x and t. 2006 provides an excellent resource in this respect.įortunately, a deep understanding of partial differential equations (PDEs) is not required to get some basic intuition about the concepts presented in this chapter. As mentioned in that chapter, implementing and debugging a 3D fluid solver is no simple task (even in a traditional programming environment), and a solid understanding of the underlying mathematics and physics can be of great help. In particular, we encourage the reader to look at Harris's chapter on 2D fluid simulation in GPU Gems (Harris 2004). Throughout this section we assume a working knowledge of general-purpose GPU (GPGPU) methods-that is, applications of the GPU to problems other than conventional raster graphics.
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