Showing papers in "Journal of Computational Physics in 2007"

TL;DR: It is proved that the full discretization is unconditionally stable, and the numerical solution converges to the exact one with order O(@Dt^2^-^@a+N^- ^m), where @Dt,N and m are the time step size, polynomial degree, and regularity of the exact solution respectively.

TL;DR: A new formulation of the immersed boundary method with a structure algebraically identical to the traditional fractional step method is presented for incompressible flow over bodies with prescribed surface motion, achieving second-order temporal accuracy and better than first-order spatial accuracy in L"2-norms for one- and two-dimensional test problems.

TL;DR: This work solves a problem of non-convex stochastic optimisation with help of simulated annealing of Levy flights of a variable stability index by solving the problem of search of the ground state of an unknown potential with non-local consequences.

TL;DR: The convective Cahn-Hilliard equation and the condition that the velocity field is divergence-free are derived from the conservation law of mass of binary mixtures in a straightforward way, for fluids with large density and viscosity ratios.

TL;DR: This work presents a reformulation of the Bayesian approach to inverse problems, that seeks to accelerate Bayesian inference by using polynomial chaos expansions to represent random variables, and evaluates the utility of this technique on a transient diffusion problem arising in contaminant source inversion.

TL;DR: It is found that slight deviations from orthogonality on the modified cubed-sphere (quasi-orthogonal) grids do not negatively impact the accuracy, and that the more uniform version of the quasi-orthogsonal cubing-spheres grids provided better overall accuracy than the most orthogonal (and therefore, much less uniform) conformal grid.

TL;DR: To obtain sharp density and viscosity discontinuities in an incompressible multi- Phase SPH flow a new multi-phase projection formulation, in which the discretized gradient and divergence operators do not require a differentiable density or viscosities field is proposed.

TL;DR: A new WENO reconstruction technique is proposed that does not reconstruct point-values but entire polynomials which can easily be evaluated and differentiated at any point and thus can be implemented very efficiently even for unstructured grids in three space dimensions.

TL;DR: The sparse grid collocation method based on the Smolyak algorithm offers a viable alternate method for solving high-dimensional stochastic partial differential equations and an extension of the collocation approach to include adaptive refinement in important stochastically dimensions is utilized to further reduce the numerical effort necessary for simulation.

TL;DR: The new method yields solutions in the zero gas density limit which are comparable in accuracy to the method in which the gas pressure was treated as spatially constant, thereby providing a speed-up over continuum or ''ghost-fluid'' methods.

TL;DR: The results obtaining by the adaptive method show good qualitative agreement with simulation results obtained by earlier non-adaptive versions of the method, but the flow in the vicinity of the model heart valves indicates that the new methodology provides enhanced boundary layer resolution.

TL;DR: The ability of the method to simulate flows with complex, moving immersed boundaries is applied to calculate pulsatile, physiological flow through a mechanical, bileaflet heart valve mounted in a model straight aorta with an anatomical-like triple sinus.

TL;DR: A Fourier method is proposed for analyzing the stability and convergence of the implicit difference approximation scheme (IDAS), derive the global accuracy of the IDAS, and discuss the solvability.

TL;DR: This numerical method combines the alternating directions implicit (ADI) approach with a Crank-Nicolson discretization and a Richardson extrapolation to obtain an unconditionally stable second-order accurate finite difference method.

TL;DR: An immersed boundary method for time-dependent, three-dimensional, incompressible flows is presented, and the predictions show good agreement with previous computational and experimental results.

TL;DR: An improved version of the immersed boundary (IB) method is developed for simulating flexible filaments in a uniform flow and a repulsive force was included in the formulation to handle collisions between the free ends of side-by-side filaments undergoing out-of-phase flapping.

TL;DR: A quadrature-free essentially non-oscillatory finite volume scheme of arbitrary high order of accuracy both in space and time for solving nonlinear hyperbolic systems on unstructured meshes in two and three space dimensions is presented.

TL;DR: An improved numerical algorithm for front tracking method is developed to simulate the rising of a bubble in quiescent viscous liquid due to buoyancy and predicted bubble shape and terminal velocity agree well with the experimental results.

TL;DR: A sharp interface capturing method is described for the study of incompressible multiphase flows with phase change using the level set method to keep track of the interface between the two phases and a ghost fluid approach to impose the jump conditions at the interface.

TL;DR: A general interface tracking method based on the phase-field equation, used to implicitly track the sharp interface on a fixed grid, without the use of separate re-initialization schemes or Lagrangian marker particles.

TL;DR: A limiter for the discontinuous Galerkin method is described that retains as high an order as possible, and does not automatically reduce to first order, and is extended to two-dimensional problems on tensor-product meshes.

TL;DR: The solver is parallelized for distributed memory platforms using domain decomposition and message passing interface (MPI) and salient features of the parallel algorithm are presented to demonstrate the ability of the solver to model complex, non-canonical three-dimensional flows.

TL;DR: This work constructs a stable high-order finite difference scheme for the compressible Navier-Stokes equations, that satisfy an energy estimate, and shows the theoretical third-, fourth-, and fifth-order convergence rate, for a viscous shock, where the analytic solution is known.

TL;DR: A weighted essentially non-oscillatory reconstruction scheme based on Hermite polynomials is developed and applied as a limiter for the discontinuous Galerkin finite element method on unstructured grids to demonstrate the accuracy, effectiveness, and robustness of the designed HWENO limiter.

TL;DR: The dispersion and dissipation properties of the matching and the boundary schemes are described in detail, and their accuracy limits are determined, to show that these schemes calculate accurately waves with at least five points per wavelength.

TL;DR: The design of bounded, higher-order convection schemes is considered with a view to selecting those discretizations giving good resolution of sharp gradients, while at the same time providing competitive accuracy and convergence behaviour when applied to smooth, recirculating flows.

TL;DR: A new multi-scale method for the homogenization analysis of hyperelastic solids undergoing finite strains, coined as reduced model multiscale method (R3M), allows reducing significantly the computation times, as no large matrix needs to be inverted and as the convergence of both macro and micro problems is enhanced.

TL;DR: The so-called ''tensile instability'' is shown to be prevented by this enhanced SPH method, through accuracy increases in the gradient approximations.

TL;DR: It is shown that the UFS can dynamically adapt the computational mesh and automatically introduce and remove kinetic patches to provide significant savings by limiting molecular scale solutions only to the regions where they are needed.

TL;DR: Here a new very high-order accurate, exactly well-balanced finite volume scheme for moving flow equilibria is presented and Numerical experiments show excellent resolution of unperturbed as well as slightly perturbedEquilibria.