This paper presents an XFEM implementation of a projection algorithm to compute in an Eulerian framework 3D incompressible two-fluid flows with arbitrary high contrasts in material properties. It is designed to deal with both strong and weak discontinuities across the interface for pressure and velocity fields, respectively. A classical enrichment function accounts for velocity gradient discontinuities across the interface and a new quadratic enrichment function accounts for pressure discontinuities across the interface. A splitting of two-fluid elements is performed to achieve accurate numerical integrations, meanwhile a scaling coefficient accounting for both physical and geometrical considerations alleviates ill-conditioning. Various validations have been carried and very good solution accuracy is achieved even on coarse meshes, as from the minimal mesh not conforming to the interface. This implementation enables to compute accurate solutions regardless of discontinuity magnitude (arbitrary high contrast in material properties) and mesh size of two-fluid elements, which can constitute a decisive advantage for large size 3D computations.

A class of nonstandard pseudospectral time domain (PSTD) schemes for solving time-dependent hyperbolic and parabolic partial differential equations (PDEs) is introduced. These schemes use the Fourier collocation spectral method to compute spatial gradients and a nonstandard finite difference scheme to integrate forwards in time. The modified denominator function that makes the finite difference time scheme exact is transformed into the spatial frequency domain or k-space using the dispersion relation for the governing PDE. This allows the correction factor to be applied in the spatial frequency domain as part of the spatial gradient calculation. The derived schemes can be formulated to be unconditionally stable, and apply to PDEs in any space dimension. Examples of the resulting nonstandard PSTD schemes for several PDEs are given, including the wave equation, diffusion equation, and convection-diffusion equation.

Gradient flows with strong anisotropic free energy are difficult to deal with numerically with existing approaches. We propose a stabilized predictor-corrector approach to construct schemes which are second-order accurate, easy to implement, and maintain the stability of first-order stabilized schemes. We apply the new approach to three different types of gradient flows with strong anisotropic free energy: anisotropic diffusion equation, anisotropic Cahn-Hilliard equation, and Cahn-Hilliard equation with degenerate diffusion mobility. Numerical results are presented to show that the stabilized predictor-corrector schemes are second-order accurate, unconditionally stable for the first two equations, and allow larger time step than the first-order stabilized scheme for the last equation. We also prove rigorously that, for the isotropic Cahn-Hilliard equation, the stabilized predictor-corrector scheme is of second-order.

A new finite element (FE) field solver has been implemented in the gyrokinetic toroidal code (GTC) in attempt to extend the simulation domain to magnetic axis and beyond the last closed flux surface, which will enhance the capability the GTC code since the original finite difference (FD) solver will lose its capability in such circumstances. A method of manufactured solution is employed in the unit fidelity test for the new FE field solver, which is then further verified through integrated tests with three typical physical cases for the comparison between the new FE field solver and the original finite difference field solver. The results by the newly implemented FE field solver are in great accord with the original solver.

This work presents a set of preconditioning strategies able to significantly accelerate the performance of fully implicit energy-conserving Particle-in-Cell methods to a level that becomes competitive with semi-implicit methods. We compare three different preconditioners. We consider three methods and compare them with a straight unpreconditioned Jacobian Free Newton Krylov (JFNK) implementation. The first two focus, respectively, on improving the handling of particles (particle hiding) or fields (field hiding) within the JFNK iteration. The third uses the field hiding preconditioner within a direct Newton iteration where a Schwarz-decomposed Jacobian is computed analytically. Clearly, field hiding used with JFNK or with the direct Newton-Schwarz (DNS) method outperforms all method. We compare these implementations with a recent semi-implicit energy conserving scheme. Fully implicit methods are still lag behind in cost per cycle but not by a large margin when proper preconditioning is used. However, for exact energy conservation, preconditioned fully implicit methods are significantly easier to implement compared with semi-implicit methods and can be extended to fully relativistic physics.

A previously developed semi-implicit method to solve a density dependent diffusion-reaction biofilm growth model on uniform Cartesian grids is extended to accommodate non-orthogonal grids in order to allow simulation on more complicated domains. The model shows two non-linear diffusion effects: it degenerates where the dependent solution vanishes, and a super-diffusion singularity where it approaches its upper bound. The governing equation is transformed to a general non-orthogonal ξ−η curvilinear coordinate system and then discretized spatially using a cell centered finite volume method. The nonlinear biomass fluxes at the faces of the control volume cell are split into orthogonal and non-orthogonal components. The orthogonal component is handled in a conventional manner, while the non-orthogonal component is treated as a part of the source term. Extensive tests showed that this treatment of the non-orthogonal flux component on the control volume face works well if the maximum deviation from orthogonality in the region of the grid where the biomass is growing is within 15-20 degrees. This range of validity is smaller than the one obtained with the same method for the simpler porous medium equation which is the standard test problem for degenerate diffusion equation but does not have all of the features of the biofilm model.

A three-field smoothed formulation is proposed in this paper for the resolution of fluid-structure interaction (FSI) from the arbitrary Lagrangian–Eulerian perspective. The idea behind the proposed approach lies in different smoothing concepts. Both fluid and solid stress tensors are smoothly treated by the cell-based smoothed finite element method (CS-FEM) using four-node quadrilateral elements. In particular, the smoothed characteristic-based split technique is developed for the incompressible flows whereas the geometrically nonlinear solid is settled through CS-FEM as usual. The deformable mesh, often represented by a pseudo-structural system, is further tuned with the aid of a hybrid smoothing algorithm. The Explicit Relaxed Interface Coupling (ERIC) scheme is presented to interpret the nonlinear FSI effect, where all interacting fields are explicitly coupled in alliance with interface relaxation method for numerical stability. The promising ERIC solver is in detail validated against the previously published data for a large-displacement FSI benchmark. The good agreement is revealed in computed results and well-known flow-induced phenomena are accurately captured.

Photoacoustic tomography is an emerging technique in biomedicine that is capable of visualizing high resolution structural and functional information of tissue up to several centimeters deep. Mesh based numerical reconstruction algorithms have an unrivaled advantage over other reconstruction algorithms in photoacoustic imaging, due to its accurate mathematical modeling and the capability to recover multiple optical/acoustic parameters in the reconstruction. However, the slow reconstruction speed and huge memory cost hindered this advanced reconstruction algorithm from application areas where large scale reconstruction or real/near-real time reconstruction is required, for example, sub-millimeter or micrometer resolution imaging, photoacoustic guided cancer treatment, etc. In this study, we reported a high performance photoacoustic tomography method based on parallel computing strategy with multiprocessor scheme. Our simulation result has shown that the parallelized photoacoustic tomography method using multiprocessor scheme is capable of providing fine reconstructed images of blood vessel structures up to 0.14mm in diameter. Further phantom experiment demonstrated that cross hairs can be clearly reconstructed, when a mesh comprised of 28512 triangle finite elements is used. Therefore, our multiprocessor based parallelized photoacoustic tomography might be promising for large scale reconstruction or real/near-real time reconstruction in biomedical application of mesh-based photoacoustic tomography algorithm.

In this work, a second-order high-resolution LAgrangian method with a Vorticity-based Adaptive Nodal Solver (LAVANS) is proposed to overcome the numerical difficulty of traditional Lagrangian methods for the simulation of multidimensional flows. The work mainly include three aspects to improve the performance of the traditional CAVEAT-type cell-centered Lagrangian method. First, a vorticity-based adaptive least-squares method for vertex velocity computation is proposed to suppress nonphysical mesh distortion caused by the traditional five-point-stencil least-squares method. Second, a simple interface flux modification is proposed such that the geometry conservation law is satisfied. Third, a generalized Riemann problem solver is employed in the LAVANS scheme to achieve one-step time-space second-order accuracy. Some typical benchmark numerical tests validate the performance of the LAVANS scheme.

For compressible flow computations, the present paper extends the ETAU (enhanced time-accurate upwind) unstructured finite volume (FV) scheme to handle curved domain boundary with better accuracy. For the interior cells in the computational domain or the boundary cells with straight line boundary, the original ETAU scheme with second order accuracy in space and time is applied. For those boundary cells with the curved geometry, a more accurate Non-Uniform Rational B-Spline (NURBS) representation of the boundary is considered. The NURBS is commonly employed in computer aided design (CAD) to construct complex geometries. Here, it yields an exact geometry expression of complex boundary geometry. By combining ETAU with NURBS, the NURBS incorporated ETAU scheme (NETAU) is proposed for more accurate geometrical representation and fluxes evaluation. Details of the computing procedure of the geometry and surface fluxes for cells on the curved boundary, such as special transformation strategies and merging of ETAU and NURBS, are introduced and implemented. With NURBS, the NETAU scheme are geometrically versatile and more flexible. Several two-dimensional (2D) numerical cases are investigated to demonstrate the performance, computing efficiency and benefits of the NETAU scheme. The numerical results show that, for flows with low speed and high Reynolds number, the NETAU scheme provides more accurate pressure distribution on curved boundary than the original ETAU scheme. Meanwhile, the high-speed flow case shows that the NETAU scheme is still stable for high Mach number problem with shocks. Thus, the NETAU scheme potentially provides an accurate tool to describe complex geometry in computational fluid dynamics (CFD) simulations. It will help to reduce computational costs and enhances accuracy for flow domain dominated by complex geometries, with features such as high curvature and sharp edges.

Identification of stable three-dimensional conformations in proteins and peptides that correspond to minima in potential and free energy hypersurfaces has been under intense scrutiny over the past decades since the paradigm structure-function was proposed [1]. This classical paradigm states that most of biologically active conformations in proteins and peptides can be associated with global minima energy states on the energy hypersurface of the polypeptide chain [2, 3]. In this work we discuss the onset of macroscopic minimum-energy conformations on small interacting peptides composed by only two types of residues: hydrophobic (A) or polar (B). Based on a previous work in 2D [4], we consider here an interacting three dimensional potential $V$ =$V_1$+$V_2$ where $V_1$ corresponds to a intramolecular bending potential between adjacent residues whereas $V_2$ is a Lennard-Jones (LJ) type intermolecular potential with both an attractive and repulsive part. In addition, the $V_2$ term can switch to repulsive or attractive depending on the type of pair interaction AA, AB or BB considered. As a novel approach to the standard geometric-based minimization methods [5–7], we propose a Multipopulation Genetic Algorithm (MpGA) as a minimization algorithm [8]. The central advantage of this approach is a wider search on the energy hypersurface. In order to test the validity of our method, we reproduced in excellent agreement the results previously obtained in 2D by [4]. Our results show that in three dimensions our method enlarges the number of stable macroscopic conformations found for a given polypeptide. As an example of the role played by the interacting pairs AB, AA and BB, we discuss as well the case of small diblock polymers and quantify the degree of compactness expected in the three dimensional structure as function of the composition of the chain.

An improved immersed boundary method is proposed and applied to simulate fluid-structure interactions by combining a level set method for free water surface capturing. An efficient Navier-Stokes equation solver adopting the fractional step method at a staggered Cartesian grid system is used to solve the incompressible fluid motion. A new efficient algorithm to search forcing points near the immersed body boundary is developed. The searching schemes for forcing points located both inside and outside the solid phase with the linear interpolation schemes for the determination of velocities at forcing points are presented and compared via the case of dam break over obstacles. The accuracy and effectiveness of the proposed forcing point searching schemes are further demonstrated by the study of wave propagation over a submerged bar and more challenging cases of wedge with prescribed velocity or falling freely into the water. By the extensive comparison of present numerical results with other experimental and numerical data, it suggests that the present improved immersed boundary method with the new forcing point searching scheme has a better performance and is very promising due to its accuracy, efficiency and ease of implementation. Furthermore, the present numerical results show that the outside forcing scheme is superior over the inside forcing scheme.

A simple C++ class structure for construction of a Monte Carlo event generator which can produce unweighted events within relativistic phase space is presented. The generator is self-adapting to the provided matrix element and acceptance cuts. The program is designed specially for exclusive processes and includes, as an example of such an application, implementation of the model for exclusive production of meson pairs $pp$→ $p$$M^+$$M^−$$p$ in high energy proton-proton collisions.

This paper presents major improvements in the efficiency of the so-called Radical-Like Polymerization (RLP) algorithm proposed in "Polymer chain generation for coarse-grained models using radical-like polymerization" [J. Chem. Phys. 128(2008)]. Three enhancements are detailed in this paper: (1) the capture radius of a radical is enlarged to increase the probability of finding a neighboring monomer; (2) between each growth step, equilibration is now performed with increasing the relaxation time depending on the actual chain size; (3) the RLP algorithm is now fully parallelized and proposed as a "fix" within the "Lammps" molecular dynamics simulation suite.