Development of a Finite Volume Particle Method for 3-D fluid flow simulations

Toward design optimization of a Pelton turbine runner

“…However, Quinlan and Nestor (2011) demonstrated that top-hat kernel allows a fast and exact computation of the interaction vector in 2-D with a circular support. In 3-D, Jahanbakhsh et al (2014) showed that the use of top-hat kernel with a rectangular support reduces significantly the cost of the integral computations in eq. (9).…”

“…They simplified the shape functions to circular top-hat kernels and achieved a reasonable compromise between computational cost and accuracy. Recently, Jahanbakhsh et al (2014) introduced rectangular top-hat kernels to compute quickly and exactly the integrals in 3-D.…”

“…FVPM combines attractive features of Smoothed Particle Hydrodynamics (SPH) and conventional grid-based Finite Volume Method (FVM). It also features the ability to include additional physics, such as silt laden flow erosion Jahanbakhsh et al (2016). Therefore, it appears as an appropriate solution for numerical estimations of the performance of Pelton runners in the presented study.…”

Enhancement of the accuracy of the finite volume particle method for the simulation of incompressible flows

“…Particles are viewed as discrete volumes, and discretized equations are very similar to those of the conventional finite volume methods. An extension of this method has been performed in many studies . Smoothed particle hydrodynamic gradient approximation is used to discretize the gradient operator for the simulation of viscous flows .…”

“…An extension of this method has been performed in many studies. 4,[25][26][27][28][29] Smoothed particle hydrodynamic gradient approximation is used to discretize the gradient operator for the simulation of viscous flows. 25,27 A simplified form of the FVP method, in which the gradient operator and the Laplacian operator are approximated on a particle surface by the interaction with neighbor particles, is used in incompressible flow simulation.…”