In this paper, we solve the force model and 3D fluid dynamics solver for surgical simulation designs by taking a combination of a cubic interpolated fluid solver and the advantage of the parallelism and programmability of GPU. In comparison to other methods, we present innovation in tree aspects. First, force models in haptic for fluid interactions is generated by GPU-CPU message passing scheme to get rapid development of haptic feedback modes for fluid dynamic data. Second, rapid solution in fluid dynamic solvers is developed by applying cubic interpolated propagation method. This method only split Navier-Stokes equations (NSEs) into advection and non-advection equation to generate immediate fluid dynamic solvers. To get more acceleration in the computation, we pack these equations into channels of texels. Third, beside we take advantage of the parallelism and programmability of the GPU where computation models are performed on pixels that can be considered to be a grid of cells, the CPU-GPU balancing is included; therefore, despite of the complexity of the anatomical geometry, processing on multiple vertices and pixels can be done simultaneously in parallel. The data are also passed to CPU to control the haptic in providing kinesthetic interaction and felling. These strategies provide effective enough to simulate fluid dynamic model for real-time interaction in 3D computer graphic for PC platform. Our experimental tests prove that fluid flowing on various obstacles with haptic interactions on the human anatomical model can be effectively and efficiently simulated on the reasonable frame rate with a realistic synthetic visualization.

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