Smoothed particle hydrodynamics (SPH) is a meshfree particle method based on Lagrangian formulation, and has been widely applied to different areas in engineering and science. This paper presents an overview on the SPH method and its recent developments, including (1) the need for meshfree particle methods, and advantages of SPH, (2) approximation schemes of the conventional SPH method and numerical techniques for deriving SPH formulations for partial differential equations such as the Navier-Stokes (N-S) equations, (3) the role of the smoothing kernel functions and a general approach to construct smoothing kernel functions, (4) kernel and particle consistency for the SPH method, and approaches for restoring particle consistency, (5) several important numerical aspects, and (6) some recent applications of SPH. The paper ends with some concluding remarks.

Smoothed Particle Hydrodynamics (SPH): an Overview and Recent Developments

Plasma–liquid interactions represent a growing interdisciplinary area of research involving plasma science, fluid dynamics, heat and mass transfer, photolysis, multiphase chemistry and aerosol science. This review provides an assessment of the state-of-the-art of this multidisciplinary area and identifies the key research challenges. The developments in diagnostics, modeling and further extensions of cross section and reaction rate databases that are necessary to address these challenges are discussed. The review focusses on non-equilibrium plasmas.

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Plasma-liquid interactions: A review and roadmap

We present two new Lagrangian methods for hydrodynamics, in a systematic comparison with moving-mesh, smoothed particle hydrodynamics (SPH), and stationary (non-moving) grid methods. The new methods are designed to simultaneously capture advantages of both SPH and grid-based/adaptive mesh refinement (AMR) schemes. They are based on a kernel discretization of the volume coupled to a high-order matrix gradient estimator and a Riemann solver acting over the volume ‘overlap’. We implement and test a parallel, second-order version of the method with self-gravity and cosmological integration, in the code gizmo:1 this maintains exact mass, energy and momentum conservation; exhibits superior angular momentum conservation compared to all other methods we study; does not require ‘artificial diffusion’ terms; and allows the fluid elements to move with the flow, so resolution is automatically adaptive. We consider a large suite of test problems, and find that on all problems the new methods appear competitive with moving-mesh schemes, with some advantages (particularly in angular momentum conservation), at the cost of enhanced noise. The new methods have many advantages versus SPH: proper convergence, good capturing of fluid-mixing instabilities, dramatically reduced ‘particle noise’ and numerical viscosity, more accurate sub-sonic flow evolution, and sharp shock-capturing. Advantages versus non-moving meshes include: automatic adaptivity, dramatically reduced advection errors and numerical overmixing, velocity-independent errors, accurate coupling to gravity, good angular momentum conservation and elimination of ‘grid alignment’ effects. We can, for example, follow hundreds of orbits of gaseous discs, while AMR and SPH methods break down in a few orbits. However, fixed meshes minimize ‘grid noise’. These differences are important for a range of astrophysical problems.

A new class of accurate, mesh-free hydrodynamic simulation methods

Numerical Modeling of Water Waves with the SPH Method

Recent advances in modeling and simulation of nanofluid flows—Part II: Applications

SPH Concept and Essential Formulation Constructing Smoothing Functions SPH for General Dynamic Fluid Flows Discontinuous SPH (DSPH) SPH for Simulating Explosions SPH for Underwater Explosion Shock Simulation SPH for Hydrodynamics with Material Strength Coupling SPH with Molecular Dynamics for Multiple Scale Simulations Computer Implementation of SPH and a 3D SPH Code.

Moubin Liu

Papers

Smoothed Particle Hydrodynamics: A Meshfree Particle Method

Smoothed Particle Hydrodynamics (SPH): an Overview and Recent Developments

Restoring particle consistency in smoothed particle hydrodynamics

Constructing smoothing functions in smoothed particle hydrodynamics with applications

An improved SPH method for modeling liquid sloshing dynamics