Related papers: Stable and accurate schemes for smoothed dissipati…
We study the asymptotic stability of the semi-discrete (SD) numerical method for the approximation of stochastic differential equations. Recently, we examined the order of $\mathcal L^2$-convergence of the truncated SD method and showed…
We present an implementation of Smoothed Particle Hydrodynamics (SPH) in an adaptive-mesh PPPM algorithm. The code evolves a mixture of purely gravitational particles and gas particles. The code retains the desirable properties of previous…
I present a review of Smoothed Particle Hydrodynamics (SPH), with the aim of providing a mathematically rigorous, clear derivation of the algorithms from first principles. The method of discretising a continuous field into particles using a…
Many relevant problems in the area of systems and control, such as controller synthesis, observer design and model reduction, can be viewed as optimization problems involving dynamical systems: for instance, maximizing performance in the…
This paper proposes a novel consistent {\delta}+- Updated Lagrangian Particle Hydrodynamics (ULPH) model. Although the Smoothed Particle Hydrodynamics (SPH) model has gained recognized achievements, it is afflicted by excessive numerical…
Generative diffusion models have achieved remarkable success in producing high-quality images. However, these models typically operate in continuous intensity spaces, diffusing independently across pixels and color channels. As a result,…
In a companion paper we have shown how the equations describing gas and dust as two fluids coupled by a drag term can be reformulated to describe the system as a single fluid mixture. Here we present a numerical implementation of the…
Many popular methods for the calculation of chemical potentials rely on the insertion of test particles into the target system. In the case of liquids and liquid mixtures, this procedure increases in difficulty upon increasing density or…
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…
Stochastic processes, in the form of stochastic differential equations (SDEs), integrate stochastic elements to account for the inherent randomness in sediment particle trajectories in an open-channel turbulent flow. Accordingly, a…
This study introduces a Riemann-based Smoothed Particle Hydrodynamics (SPH) framework for the stable and accurate simulation of surface tension in multiphase flows, with density and viscosity ratios as high as 1000 and 100, respectively.…
The algorithm for Dissipative Particle Dynamics (DPD), as modified by Espagnol and Warren, is used as a starting point for proving an H-theorem for the free energy and deriving hydrodynamic equations. Equilibrium and transport properties of…
To capture specific characteristics of non-Newtonian fluids, during the past years fractional constitutive models have become increasingly popular. These models are able to capture in a simple and compact way the complex behaviour of…
We analyzed extensively the dynamics of polymer chains in solutions simulated with dissipative particle dynamics (DPD), with a special focus on the potential influence of a low Schmidt number of a typical DPD fluid on the simulated polymer…
A three-dimensional model is presented for the prediction of solidification behavior using a nonlinear transformation of the enthalpy equation in a Smoothed Particle Hydrodynamics (SPH) discretization. The effect of phase change in the form…
Conformal energy minimization is an efficient approach to compute conformal parameterization. In this paper, we develop a stable algorithm to compute conformal parameterization of simply connected open surface, termed Stable Discrete…
We develop a method for simulating colloidal suspensions using multiparticle collision dynamics (MPCD) with a discrete particle model represented as a rigid body. The key steps for incorporating the rigid-body constraints are to thermalize…
In this work, we design an entropy stable, finite volume approximation for the shallow water magnetohydrodynamics (SWMHD) equations. The method is novel as we design an affordable analytical expression of the numerical interface flux…
The stochastic differential equations for a model of dissipative particle dynamics, with both total energy and total momentum conservation at every time-step, are presented. The algorithm satisfies detailed balance as well as the…
We present and test a general-purpose code, called PPASPH, for evolving self-gravitating fluids in astrophysics, both with and without a collisionless component. In PPASPH, hydrodynamical properties are computed by using the SPH (Smoothed…