A computer implemented method of simulating a real-world system of a motion of a physical object through an incompressible fluid, the method is performed by a central processing unit using a memory and a display device, the method comprising: - generating, by the central processing unit and in the memory, in response to a user interaction defining properties of the real-world system a time dependent system of equations representing an approximation of the physics of the real-world system of the motion of the physical object through the incompressible fluid, the time dependent system of equations having a defined constraint, the constraint being incompressibility of the fluid surrounding the physical object; - de-coupling, by the central processing unit and in the memory, the constraint from the time dependent system of equations using a matrix representing an approximation of physics of the real-world system, the de-coupling generating a first system of equations representing the constraint and a second system of equations representing physics of the physical object of the real-world system; - solving, by the central processing unit and in the memory, the generated first system of equations and the generated second system of equations entirely without computing an inverse of a Jacobian matrix J -1 associated with the time dependent system of equations; and - simulating the real-world system by generating a simulation of the real-world system using results from solving the generated first and second systems of equations, the simulating including visually illustrating, to a user and via the display device, a simulation of the motion of the physical object of the real-world system based on the solving. - generating, by the central processing unit and in the memory, in response to a user interaction defining properties of the real-world system a time dependent system of equations representing an approximation of the physics of the real-world system of the motion of the physical object through the incompressible fluid, the time dependent system of equations having a defined constraint, the constraint being incompressibility of the fluid surrounding the physical object; - de-coupling, by the central processing unit and in the memory, the constraint from the time dependent system of equations using a matrix representing an approximation of physics of the real-world system, the de-coupling generating a first system of equations representing the constraint and a second system of equations representing physics of the physical object of the real-world system; - solving, by the central processing unit and in the memory, the generated first system of equations and the generated second system of equations entirely without computing an inverse of a Jacobian matrix J -1 associated with the time dependent system of equations; and - simulating the real-world system by generating a simulation of the real-world system using results from solving the generated first and second systems of equations, the simulating including visually illustrating, to a user and via the display device, a simulation of the motion of the physical object of the real-world system based on the solving.