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• Unstable pressure computation investigated from a totally new viewpoint of particle-level contact/collisions. • Proposition of correction based on momentum conservation of particle-level collisions. • New stable source terms are derived for pressure Poisson equation (PPE), mitigating pressure oscillations in a wider range of time and spatial resolutions. • Very simple implementation and no additional computational effort, which are desirable for practical engineering applications. • The approach can be combined with other strategies and incorporate into other projected-based particle methods. • Extensive verifications through hydrostatic and hydrodynamic benchmarks. The aim of this paper is to investigate the unstable nature of pressure computation focusing on incompressible flow modeling through the projection-based particle methods. A new approach from the original viewpoint of the momentum conservation regarding particle-level collisions, hereinafter refered to as time-scale correction of particle-level impulses (TCPI), is proposed to derive new source terms of pressure Poisson equation (PPE). This results in more stable computations with drastic reduction of unphysical pressure oscillations and more robust simulation with pressure magnitudes almost independent to time step. Moreover, compared to other strategies, no additional computational effort is required, its implementation is extremely simple, and the only numerical parameter is the propagation speed of the perturbations, of which the calibration is much more straightforward due to its physical meaning. Simulations were carried out using moving particle semi-implicit (MPS) method improved by the proposed approach. The comparisons of computed results with theoretical and experimental ones confirmed the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

As a Lagrangian type meshless method, the MPS is suitable for violent free surface problems. In this paper, for problems where violent free surface deformation only occur in a constrained area, the efficiency of MPS is further improved by weak coupling with BEM. More specifically, the whole computational domain is modeled by BEM whereas the MPS model only covers the violent flow area. Since the computational time of BEM is negligible compared with the time required by MPS, the overall computational efficiency could be improved by this coupling scheme (depends on how much of the MPS domain is replaced by BEM). The MPS model is advanced by the information from BEM result at each time step up to the time when the free surface is about to break. The MPS solver will continue the simulation with the “old” BEM information just before breaking, based on the assumption that the flow change at the MPS–BEM interface area is small enough. The proposed scheme is validated by two problems and a relatively good accuracy is obtained by comparing with published results in the literature. [ABSTRACT FROM AUTHOR]

A new particle method is proposed for computing incompressible flows. Using Moving Particle Semi-implicit (MPS) and Smoothed Particle Hydrodynamics (SPH) approaches, a new Moving Particle Explicit (MPE) method is developed. The concept, like the MPS method, is based on the weighted averaging scheme. Introducing a directional particle number density, the derivation of spatial discretization is performed without imposing any simplification. As a consequence, the formulation becomes more generic and covers the MPS scheme. The solution algorithm is similar to the weakly compressible SPH method. Considering slight compressibility for an incompressible flow, the continuity equation for compressible flow together with an equation of state is used to decouple the velocity and pressure of the Navier–Stokes equations. Consequently, the method becomes fully explicit, and the problems related to solving a set of equations in an implicit procedure are removed. Easy application of the solution algorithm, in comparison with the MPS method, as well as the generic discretization scheme, makes the MPE method more efficient for simulating incompressible flows. The proposed method is validated using a Poiseuille flow and two dam break problems; furthermore, a submerged hydraulic jump is investigated to evaluate the method’s capability in simulating open boundary problems. In all cases, good agreement between numerical results and analytical/experimental data is observed. [ABSTRACT FROM AUTHOR]

The density-matrix renormalization group method has become a standard computational approach to the low-energy physics as well as dynamics of low-dimensional quantum systems. In this paper, we present a new set of applications, available as part of the ALPS package, that provide an efficient and flexible implementation of these methods based on a matrix product state (MPS) representation. Our applications implement, within the same framework, algorithms to variationally find the ground state and low-lying excited states as well as simulate the time evolution of arbitrary one-dimensional and two-dimensional models. Implementing the conservation of quantum numbers for generic Abelian symmetries, we achieve performance competitive with the best codes in the community. Example results are provided for (i) a model of itinerant fermions in one dimension and (ii) a model of quantum magnetism. Program summary Program title: ALPS MPS Catalogue identifier: AEUL_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEUL_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Use of ‘mps optim’, ‘mps tevol’, ‘mps meas’ or ‘mps overlap’ requires citation of this paper. Use of any ALPS program requires citation of the ALPS [1] paper. No. of lines in distributed program, including test data, etc.: 373799 No. of bytes in distributed program, including test data, etc.: 2019043 Distribution format: tar.gz Programming language: C++, OpenMP for parallelization. Computer: PC, HPC cluster. Operating system: Any, tested on Linux, Mac OS X and Windows. Has the code been vectorized or parallelized?: Parallelized using OpenMP 1 to 24 processors used. RAM: 100 MB–100 GB. Classification: 7.7. External routines: ALPS [1, 2], BLAS/LAPACK, HDF5. Nature of problem: Solution of quantum many-body systems is generally a hard problem. The many-body Hilbert space grows exponentially with the system size which limits exact diagonalization results to only 20–40 spins, and the fermionic negative sign problem limits the Quantum Monte Carlo methods to a few special cases. Solution method: The matrix product states ansatz provides a controllable truncation of the Hilbert space which makes it currently the method of choice to investigate low-dimensional systems in condensed matter physics. Our implementation allows simulation of arbitrary one-dimensional and two-dimensional models and achieves performance competitive with the best codes in the community. We implement conservation of quantum numbers for generic Abelian symmetries. Running time: 10 s–8h per sweep. References: [1] B. Bauer, et al. (ALPS Collaboration), The ALPS project release 2.0: open source software for strongly correlated systems, J. Stat. Mech. 2011 (05) (2011) P05001. http://dx.doi.org/10.1088/1742-5468/2011/05/P05001 . [2] http://alps.comp-phys.org . [ABSTRACT FROM AUTHOR]

Abstract: We consider approximate computation of several minimal eigenpairs of large Hermitian matrices which come from high-dimensional problems. We use the tensor train (TT) format for vectors and matrices to overcome the curse of dimensionality and make storage and computational cost feasible. We approximate several low-lying eigenvectors simultaneously in the block version of the TT format. The computation is done by the alternating minimization of the block Rayleigh quotient sequentially for all TT cores. The proposed method combines the advances of the density matrix renormalization group (DMRG) and the variational numerical renormalization group (vNRG) methods. We compare the performance of the proposed method with several versions of the DMRG codes, and show that it may be preferable for systems with large dimension and/or mode size, or when a large number of eigenstates is sought. [Copyright &y& Elsevier]

Abstract: The analogies between the Moving Particle Semi-implicit method (MPS) and Incompressible Smoothed Particle Hydrodynamics method (ISPH) are established in this note, as an extension of the MPS consistency analysis conducted in Souto-Iglesias et al. (2013). [Copyright &y& Elsevier]

Abstract: The consistency of the Moving Particle Semi-implicit (MPS) method in reproducing the gradient, divergence and Laplacian differential operators is discussed in the present paper. Its relation to the Smoothed Particle Hydrodynamics (SPH) method is rigorously established. The application of the MPS method to solve the Navier–Stokes equations using a fractional step approach is treated, unveiling inconsistency problems when solving the Poisson equation for the pressure. A new corrected MPS method incorporating boundary terms is proposed. Applications to one dimensional boundary value Dirichlet and mixed Neumann–Dirichlet problems and to two-dimensional free-surface flows are presented. [Copyright &y& Elsevier]

Abstract: In order to investigate the effects of an elastically-linked moving body on liquid sloshing inside a tank, an analytical formulation and a numerical approach were proposed to assess hydrodynamic loads in a partially filled rectangular tank with a body connected to the tank by springs. The analytical approach was developed based on the potential theory to calculate fluid velocity field, and the dynamics of the liquid sloshing coupled to the moving body are described as a mechanical system with two degrees of freedom. The coupling between the fluid and the moving body is given by a damping force calculated based on the body geometry and the fluid velocity field. The proposed numerical approach is based on the Moving Particle Semi-implicit (MPS) method, which is a Lagrangian particle-based method and very effective to model nonlinear hydrodynamics due to fluid–structure interaction. In the numerical approach, the rigid body is modeled as a cluster of particles and the motions are calculated considering its mass, moment of inertia, hydrodynamic loads and springs restoring forces. The elastic link between the body and tank is modeled by applying Hooke’s law. Simple cases of floating body motion were used to validate the numerical method. Finally, analytical and numerical results were compared. Despite its simplicity, the analytical approach proposed in the present work is an efficient approach to provide qualitative understanding and a first estimate of the moving body effects on the sloshing inside the tank. On the other hand, the numerical approach can provide more detailed information about the coupling phenomena, and it is an effective mean for the assessment of the reduction of the sloshing loads due to the moving body with elastic link. Finally, the effectiveness of the concept as a sloshing suppressing device is also investigated. [Copyright &y& Elsevier]

Abstract: In this paper we apply the newly developed method of particular solutions (MPS) and one-stage method of fundamental solutions (MFS-MPS) for solving fourth-order partial differential equations. We also compare the numerical results of these two methods to the popular Kansa''s method. Numerical results in the 2D and the 3D show that the MFS-MPS outperformed the MPS and Kansa''s method. However, the MPS and Kansa''s method are easier in terms of implementation. [Copyright &y& Elsevier]

• An explicit weakly compressible MPS method, referred to as WCMPE is developed. • WCMPE is advantageous on simple algorithm, high computational efficiency and simulation accuracy. • WCMPE combined the divergence-free condition with mixed source Poisson pressure equation (PPE) condition by half-step pressure through equation of state. Moving particle simulation (MPS) is a Lagrange meshless method capable of simulating complex fluid problems. To improve computational efficiency with a simple algorithm, explicit algorithms have been proposed such as the Weakly Compressible MPS (WCMPS) method. Although accuracy can be fulfilled in WCMPS, instability arises due to pressure fluctuations of the moving particles. In this study, an explicit Poisson Pressure Equation (PPE) was introduced to address particle instability by improving the pressure calculation, referred to as the Weakly Compressible Moving Particle Explicit (WCMPE) method. By predicting pressure through the equation of state for WCMPS, divergence-free condition is conserved without the implementation of small time-steps. Several numerical cases were investigated by the WCMPE method, including 2D jet imping on a solid plate case, oscillating drop, lid driven cavity, rolling tank experiment, sloshing tank simulation and jet impinging from the bottom of a tank. In general, smooth pressure distribution and improved particle stability were obtained with the incorporation of WCMPE. [ABSTRACT FROM AUTHOR]

Lattice models consisting of high-dimensional local degrees of freedom without global particle-number conservation constitute an important problem class in the field of strongly correlated quantum many-body systems. For instance, they are realized in electron-phonon models, cavities, atom-molecule resonance models, or superconductors. In general, these systems elude a complete analytical treatment and need to be studied using numerical methods where matrix-product states (MPSs) provide a flexible and generic ansatz class. Typically, MPS algorithms scale at least quadratic in the dimension of the local Hilbert spaces. Hence, tailored methods, which truncate this dimension, are required to allow for efficient simulations. Here, we describe and compare three state-of-the-art MPS methods each of which exploits a different approach to tackle the computational complexity. We analyze the properties of these methods for the example of the Holstein model, performing high-precision calculations as well as a finite-size-scaling analysis of relevant ground-state observables. The calculations are performed at different points in the phase diagram yielding a comprehensive picture of the different approaches. [ABSTRACT FROM AUTHOR]