The non-symmetrical collapse of an empty cylindrical cavity is modelled using Smoothed Particle Hydrodynamics. The presence of a nearby surface produces an anisotropic pressure field generating a high velocity jet that hits the surface. The collapse follows a different dynamic based to the initial distance between the centre of the cavity and the surface. When the distance is greater than the cavity radius (detached cavity) the surface is hit by travelling shock waves. When the distance is less than the cavity radius (attached cavity) the surface is directly hit by the jet and later by other shock waves generated in the last stages of the of the collapse. The results show that the surface is hit by a stronger shock when distance between the centre of the cavity and the surface is zero while showing more complex double peaks behaviour for other distances.

Meshfree particle method, which is always regarded as a pure Lagrangian approach, is easily represented complicated domain topologies, moving boundaries, and multiphase media. Solving acoustic problems with the mesfree particle method forms a branch of the acoustic wave modeling field, namely, particle-based computational acoustics (PCA). The aim of this paper is to improve the accuracy of using the PCA method to solve two-dimensional acoustic problems, and realize the particle representation with a hybrid meshfree and finite-difference time-domain (FDTD) method for acoustic boundary conditions at both the plane and curved surface. As a widely used Lagrangian meshfree method, the smoothed particle hydrodynamics (SPH) based on the support domain and the kernel function has developed rapidly in recent years. The traditional SPH method is easily implements parallel processing and has been applied in sound wave simulation. As a corrective method with higher accuracy than SPH, the acoustic propagation and scattering in the time domain is simulated with the corrective smoothed particle method (CSPM). Moreover, a hybrid meshfree-FDTD boundary treatment technique is utilized to represent different acoustic boundaries in the Lagrangian approach. In this boundary treatment technique, the parameter value of virtual particles is obtained with the FDTD method, which concerns truncation errors based on the Tayler series expansion. Soft, rigid, and Mur’s absorbing boundary conditions are developed to simulate sound waves in finite and infinite domain. Results of modeling acoustic propagation and scattering show that CSPM is accurate and convergence with exact solutions, and different acoustic boundaries are validated to be effective in the computation.

The development of computational acoustics allows simulation of sound generation and propagation in complex environment. In particular, meshfree methods are widely used to solve acoustics problems through arbitrarily distributed field points and approximation smoothness flexibility. As a Lagrangian meshfree method, smoothed particle hydrodynamics (SPH) method reduce the difficulty in solving problems with deformable boundaries, complex topologies, or multiphase medium. The traditional SPH method has been applied in acoustic simulation. This study presents the corrective smoothed particle method (CSPM), which is a combination of SPH kernel estimate and Taylor series expansion. The CSPM is introduced as a Lagrangian approach to improve accuracy in solving acoustic wave equations in the time domain. Moreover, a boundary treatment technique based on the hybrid meshfree and finite difference time domain (FDTD) method is proposed to represent different acoustic boundaries with particles. To model sound propagation in pipes with different boundaries, soft, rigid, and absorbing boundary conditions are built with this technique. Numerical results show that the CSPM algorithm is consistent and demonstrates convergence with exact solutions. Main computational parameters are discussed, and different boundary conditions are validated to be effective for benchmark problems in computational acoustics.

The proximal part of the colon offers opportunities to prolong the absorption window following oral administration of a drug. In this work, we used computer simulations to understand how the hydrodynamics in the proximal colon might affect the release from dosage forms designed to target the colon. For this purpose, we developed and compared three different models: a completely-filled colon, a partially-filled colon and a partially-filled colon with a gaseous phase present (gas-liquid model).The highest velocities of the liquid were found in the completely-filled model, which also shows the best mixing profile, defined by the distribution of tracking particles over time. No significant differences with regard to the mixing and velocity profiles were found between the partially-filled model and the gas-liquid model. The fastest transit time of an undissolved tablet was found in the completely-filled model. The velocities of the liquid in the gas-liquid model are slightly higher along the colon than in the partially-filled model. The filling level has an impact on the exsisting shear forces and shear rates, which are decisive factors in the development of new drugs and formulations.

This work presents a linear smoothing scheme over high-order triangular elements in the framework of a cell-based strain smoothed finite element method for two-dimensional nonlinear problems. The main idea behind the proposed linear smoothing scheme for strain-smoothed finite element method (S-FEM) is no subdivision of finite element cells to sub-cells while the classical S-FEM needs sub-cells. Since the linear smoothing function is employed, S-FEM is able to use quadratic triangular or quadrilateral elements. The modified smoothed matrix obtained node-wise is evaluated. In the same manner with the computation of the strain-displacement matrix, the smoothed stiffness matrix and deformation graident are obtained over smoothing domains. A series of benchmark tests are investigated to demonstrate validity and stability of the proposed scheme. The validity and accuracy are confirmed by comparing the obtained numerical results with the standard FEM using 2nd-order triangular element and the exact solutions.

In this paper, we first discuss the research status and application progress of the finite element method and the smoothed particle method. By analyzing the advantages of the smoothed particle method and the finite element method, a new coupling algorithm, namely FEM-SPH algorithm, is proposed. By the method of comparison, it shows that finite element method and SPH method in the simulation of large deformation problems each have advantages and disadvantages, the finite element method smoothed particle coupling algorithm is effective to achieve the performance of high computational efficiency and can naturally simulate large deformation problems across. In the process of calculation, the large deformation unit can be freely into an algorithm to facilitate the calculation accuracy and efficiency of three methods of numerical simulation. Through the study found, FEM-SPH algorithm not only overcome the defect of smooth particle tensile instability, but also overcomes the problem of low efficiency of finite element computation. To further test the FEM-SPH algorithm has advantages in the practical engineering, we have carried out the actual test to the example of the super high speed collision, concluded that, since the target of most of the computational domain is always finite element, smoothed particle focused only in contact with the projectile and target of local area, particle number is not much, the whole calculation process just ten minutes, computational efficiency has been greatly improved, at the same time in the simulation of large deformation, the advantage is very obvious .This provides a criterion for the actual project, depending on the specific material deformation mode and choose a more appropriate conversion algorithm.

The extensive use of carrier-aided smoothing code (CSC) filter has led to reduce the noise level of raw code measurements in GNSS positioning and navigation applications. However, the existing CSC technique is sensitive to the changes of the integer ambiguity and then the smoothing proce-dure needs to be restarted in the presence of cycle-slips. As the Doppler shift is instantaneous ob-servation and immune to cycle-slips, Doppler-aided smoothing code (DSC) algorithm would be more promising in challenged environment. Based on the Hatch-filter, an optimal DSC approach is proposed with the principle of minimum variance. Meanwhile, to inhibit the effect of integral cumulative error of Doppler, a balance factor is adopted to adjust the contributions of raw code and DSC. The noise level of code observable is not only affected by thermal noise, but also limited by systematic bias. Satellite code bias (SCB) has been identified in the raw code observable on each frequency for each BDS-2 satellite. By minimizing the sum of absolute value of residuals, polyno-mial segment fitting algorithm as a function of elevation-angles is applied to establish the SCB cor-rection model based on epoch-differenced Multipath (MP) deviations. Finally, numerical experi-ments demonstrate the validity and efficiency of the refined DSC filter with SCB corrections on each available frequency for BDS-2 un-GEO satellites.

This study proposes a 3D particle-base (discrete) multiphysics approach for modelling calcification in the aortic valve. Different stages of calcification (from mild to severe) were simulated, and their effect on the cardiac output assessed. The cardiac flow rate decreases with the level of calcification. In particular, there is a critical level of calcification below which the flow rate decreases dramatically. Mechanical stress on the membrane is also calculated. The results show that, as calcification progresses, spots of high mechanical stress appear. Firstly, they concentrate in the regions connecting two leaflets; when severe calcification is reached, then they extend to the area at the basis of the valve.

Although Eulerian approaches are standard in computational acoustics, they are less effective for certain classes of problems like bubble acoustics and combustion noise. A different approach for solving acoustic problems is to compute with individual particles following particle motion. In this paper, a Lagrangian approach to model sound propagation in moving fluid is presented and implemented numerically, using three meshfree methods to solve the Lagrangian acoustic perturbation equations (LAPE) in the time domain. The LAPE split the fluid dynamic equations into a set of hydrodynamic equations for the motion of fluid particles and perturbation equations for the acoustic quantities corresponding to each fluid particle. Then, three meshfree methods, the smoothed particle hydrodynamics (SPH) method, the corrective smoothed particle (CSP) method, and the generalized finite difference (GFD) method, are introduced to solve the LAPE and the linearized LAPE (LLAPE). The SPH and CSP methods are widely used meshfree methods, while the GFD method based on the Taylor series expansion can be easily extended to higher orders. Applications to modeling sound propagation in steady or unsteady fluids in motion are outlined, treating a number of different cases in one and two space dimensions. A comparison of the LAPE and the LLAPE using the three meshfree methods is also presented. The Lagrangian approach shows good agreement with exact solutions. The comparison indicates that the CSP and GFD method exhibit convergence in cases with different background flow. The GFD method is more accurate, while the CSP method can handle higher Courant numbers.