In this report we present performance measurements of our parallel predictive-corrective incompressible SPH (PCISPH) implementation. PCISPH is an incompressible fluid simulation method based on the Lagrangian SPH model. In this method, incompressibility is enforced by using a prediction-correction scheme to determine the particle pressures. The information about density fluctuations is actively...

We present an implementation of Smoothed Particle Hydrodynamics (SPH) in an adaptive-mesh P 3 M algorithm. The code evolves a mixture of purely gravitational particles and gas particles. SPH gas forces are calculated in the standard way from near neighbours. Gravitational forces are calculated using the mesh reenement scheme described by Couchman (1991). The AP 3 M method used in the code gives...

Smoothed Particle Hydrodynamics is a multidimensional Lagrangian method of numerical hydrodynamics that has been used to tackle a wide variety of problems in astrophysics. Here we develop the basic equations of the SPH scheme, and we discuss some of its numerical properties and limitations. As an illustration of typical astrophysical applications, we discuss recent calculations of stellar inter...

In this paper we present some test results of our newly developed Multi-Phase Chemo-Dynamical Smoothed Particle Hydrodynamics (MP-CD-SPH) code for galaxy evolution. At first, we present a test of the “pure” hydro SPH part of the code. Then we describe and test the multi-phase description of the gaseous components of the interstellar matter. In this second part we also compare our condensation a...

We describe a modified form of Smoothed Particle Hydrodynamics (SPH) in which the specific thermal energy equation is based on a compatibly differenced formalism, guaranteeing exact conservation of the total energy. We compare the errors and convergence rates of the standard and compatible SPH formalisms on analytic test problems involving shocks. We find that the new compatible formalism relia...

We present a novel boundary handling scheme for incompressible fluids based on Smoothed Particle Hydrodynamics (SPH). In combination with the predictive-corrective incompressible SPH (PCISPH) method, the boundary handling scheme allows for larger time steps compared to existing solutions. Furthermore, an adaptive time-stepping approach is proposed. The approach automatically estimates appropria...

A simple short proof of the Johnson-Lindenstrauss lemma (concerning nearly isometric embeddings of finite point sets in lower-dimensional spaces) is given. This result is applied to show that if G is a graph on n vertices and with smallest eigenvalue i then its sphericity sph(G) is less than cA2 log n. It is also proved that if G or its complement is a forest then sph(G) < c log n holds. Q 19%8...

In this paper, we present two different techniques to accelerate and approximate particle-based fluid simulations. The first technique identifies and employs larger time steps than dictated by the CFL condition. The second introduces the concept of approximation in the context of particle advection. For that, the fluid is segregated into active and inactive particles, and a significant amount o...