SPH-based Model Research Articles

Study and application of pollutant diffusion based on SPH method

In this paper, the meshless smooth particle hydrodynamics (SPH) method is used to simulate the transport process of pollutants in the environment by solving the convection-diffusion equation of pollutants under the Lagrangian framework. This method avoids various numerical problems caused by mesh distortion or mesh movement and the calculation of the derivative of the kernel function when approximating the second derivative kernel. In order to reduce the original virtual particle method of SPH to solve the boundary problem due to the large amount of particle searches will increase the amount of redundant calculation and other factors, selected with the finite difference method to solve the boundary. To verify the proposed Lagrangian particle model, numerical experiments were carried out. The one-dimensional calculation results are compared in detail with the results of different schemes in the finite difference method, and the L2, L∞ and relative errors are analyzed. The simulation results show that the SPH-based model requires fewer particles. In addition, the model is numerically analyzed under the condition of ensuring accuracy. The numerical solution is in good agreement with the analytical solution. The research results of this paper can provide a new solution and idea for environmental pollution early warning.

Simulation of random wave overtopping by a WCSPH model

In this work the Weakly Compressible SPH-based (WCSPH) model DualSPHysics has been validated and applied to study the random wave overtopping of dike-promenade layout in shallow water conditions. Data from physical model tests carried out in a small-scale wave flume have been used for model validation. The results have been compared in terms of water surface elevation, mean discharges and individual overtopping volumes distribution. The selected geometrical layout is representative of the coastal area of Premià de Mar, in Catalonia (Spain). This stretch of the coast presents both railways and a bike path very close to the shore and therefore exposed to possible sea storms. For the first time an SPH-based model has been employed to reproduce long-lasting wave overtopping tests, made of time series of 1000 irregular waves, which are representative of real sea states. The density diffusion scheme and the modified Dynamic Boundary Conditions have been applied in the present simulations. By employing standard setup for SPH modelling of wave-structure interaction problems of a very long duration, stable simulations and accurate results have been attained.

Coastal pollutant transport modeling using smoothed particle hydrodynamics with diffusive flux

The Smoothed Particle Hydrodynamics (SPH) method is used in this paper to simulate the transport process of coastal pollutant by solving the two-dimensional (2D) depth averaged advection-diffusion equation in Lagrangian framework. To avoid directly discretizing the second-order derivatives, the diffusion terms are decomposed into two first-order derivatives by introducing the diffusive flux. To verify the proposed Lagrangian particle model, numerical experiments on four typical tests are performed, including the discontinuity, pure advection, grid anisotropy and large deforming flow. The high-resolution Total Variation Diminishing (TVD) scheme - the modified TVD Lax–Friedrichs method with Superbee limiter (MTVDLF-Superbee) - is also implemented for detailed comparison. The simulation results indicated that the present SPH-based model has better performance than MTVDLF-Superbee. In addition, the stability, convergence and efficiency of the proposed model are numerically analyzed. The Lagrangian particle model with diffusive flux gives satisfactory results with big time step and hence allows large Courant number, guaranteeing the computational efficiency.

Towards a more complete tool for coastal engineering: solitary wave generation, propagation and breaking in an SPH-based model

ABSTRACTThe present work describes the implementation of an advanced solitary wave generation system in the mesh-less SPH-based DualSPHysics model to simulate tsunami-like solitary waves. Three different generation theories have been implemented and are extended to generate multiple solitary waves. The numerical model is validated against theoretical solutions and physical model results from three different experimental campaigns, which investigated respectively: i) the forces exerted on harbour protections; ii) the run-up of solitary waves on a gentle beach; and iii) the impact of double solitary waves on two cylindrical reservoirs. The differences of modelling breaking and non-breaking wave conditions are highlighted. The results demonstrate the capability of DualSPHysics to represents the main hydrodynamic properties of solitary waves when interacting with the shoreline or with coastal structures. The applicability of DualSPHysics to coastal engineering problems is enhanced, being the model already capable of generating monochromatic waves and random sea states.

Improved relaxation zone method in SPH-based model for coastal engineering applications

An improved Relaxation Zone (RZ) method has been implemented in the meshless SPH-based DualSPHysics model. Final purpose of this work is to have a general wave generation scheme that allows coupling SPH-based models to other models, e.g. Eulerian based wave models, besides employing the RZ as alternative wave generation in SPH as a stand-alone scheme. Using RZ in SPH, the movement of the fluid particles is controlled by correcting their orbital velocity by means of a weighting function in a specified generation area. In the present work, the new technique is used to couple DualSPHysics to the non-hydrostatic wave-flow model SWASH. The results of RZ employed both as stand-alone wave generation technique and as coupling framework with SWASH model are validated for wave generation and wave reflection for monochromatic waves. Then, the method is tested successfully for generation and absorption of irregular waves. Finally, the coupling between DualSPHysics and SWASH using RZ is validated against experimental data concerning the wave flow impacts on vertical walls. A procedure for a proper design of the RZ (i.e. shape of the weighting function, size of the RZ) is described in the present work. Overall, the results indicate that the proposed improved RZ technique is among the most effective alternatives for wave generation in SPH-based models for coastal engineering application.