Showing papers in "Journal of Computational Physics in 2010"

TL;DR: High order accurate discontinuous Galerkin (DG) schemes which preserve positivity of density and pressure for Euler equations of compressible gas dynamics are constructed and extended to higher dimensions on rectangular meshes.

TL;DR: It is shown that the same limiter can preserve the maximum principle for DG or finite volume schemes solving two-dimensional incompressible Euler equations in the vorticity stream-function formulation, or any passive convection equation with an incompressibles velocity field.

TL;DR: The results indicate that the WENO methods provide sharp shock profiles, but overwhelm the physical dissipation, and the hybrid method is minimally dissipative and leads to sharp shocks and well-resolved broadband turbulence, but relies on an appropriate shock sensor.

TL;DR: A general time-discrete framework to design asymptotic-preserving schemes for initial value problem of the Boltzmann kinetic and related equations, which can capture the macroscopic fluid dynamic (Euler) limit even if the small scale determined by the Knudsen number is not numerically resolved.

TL;DR: A lattice Boltzmann equation (LBE) method for incompressible binary fluids is proposed to model the contact line dynamics on partially wetting surfaces, which is commonly encountered in drop-on-demand inkjet applications.

TL;DR: This paper develops a fast finite difference method for fractional diffusion equations, which only requires storage of O(N) and computational cost of O (Nlog^2N) while retaining the same accuracy and approximation property as the regular finite Difference method.

TL;DR: The proposed method has the same functional capabilities as a structural optimization method based on the level set method incorporating perimeter control functions and is applied to two-dimensional linear elastic and vibration optimization problems such as the minimum compliance problem, a compliant mechanism design problem and the eigenfrequency maximization problem.

TL;DR: An asymptotic analysis of the model equation with boundary rules for the Dirichlet and Neumann-type (specified flux) conditions is carried out to show that the model is first- and second-order accurate in time and space, respectively.

TL;DR: It is shown that the RBVMS formulation globally conserves angular momentum, a feature that is felt to be important for flows dominated by rotation, and that is not shared by standard stabilized formulations of fluid flow.

TL;DR: A high-order finite-element application, which performs the numerical simulation of seismic wave propagation resulting from earthquakes at the scale of a continent or from active seismic acquisition experiments in the oil industry, on a large cluster of NVIDIA Tesla graphics cards using the CUDA programming environment and non-blocking message passing based on MPI.

TL;DR: A numerical scheme applicable to arbitrarily-structured C-grids is presented for the nonlinear shallow-water equations, using the vector-invariant form of the momentum equation to guarantee that mass, velocity and potential vorticity evolve in a consistent and compatible manner.

TL;DR: A number of numerical examples suggest that the present scheme, while preserving the good shock-capturing properties of the classical WENO schemes, achieves very small numerical dissipation.

TL;DR: A method to stabilize simulations and suppress the pressure oscillation in Moving Particle Semi-implicit method for an incompressible fluid is presented and the Quasi-Compressibility is also introduced for stabilization.

TL;DR: A high-order discontinuous Galerkin (dG) scheme for the numerical solution of three-dimensional wave propagation problems in coupled elastic-acoustic media is introduced, and consistency and stability of the proposed dG scheme are proved.

TL;DR: A new reproducing divergence approximation without the need for a matrix inversion is derived and a density-weighted color-gradient formulation is introduced to reflect the reality of an asymmetrically distributed surface-tension force.

TL;DR: A strategy to design locally conservative finite-difference approximations of convective derivatives for shock-free compressible flows with arbitrary order of accuracy that can be applied as a building block of low-dissipative, hybrid shock-capturing methods.

TL;DR: The proposed method provides accurate results for stochastic dimensionality as high as 500 even with large-input variability and the efficiency of the proposed method is examined by comparing with Monte Carlo (MC) simulation.

TL;DR: Computational experiments confirm robustness of the algorithm with respect to its internal parameters and demonstrate significant increase of the convergence rate for problems with high-contrast coefficients at a low overhead per iteration.

TL;DR: The localized artificial diffusivity method is investigated in the context of large-eddy simulation of compressible turbulent flows and the proposed combination of Ducros-type sensor with a negative dilatation sensor removes unnecessary bulk viscosity within expansion and weakly compressible turbulence regions without shocks and allows it to localize near the shocks.

TL;DR: Conservative methods for the numerical solution of the Vlasov equation are developed in the context of the one-dimensional splitting and present an alternative to the traditional semi-Lagrangian schemes which can suffer from bad mass conservation, in this time splitting setting.

TL;DR: A novel algorithm to detect the free-surface in particle simulations, both in two and three dimensions, based on SPH interpolations, which can be easily embedded in SPH solvers, without a significant increase of the CPU time.

TL;DR: The multi-element probabilistic collocation method MEPCM is employed to enhance the convergence rate of polynomial chaos in high dimensions and in problems with low stochastic regularity, and it is found to be more efficient for up to 600 dimensions for a specific multi-dimensional integration problem involving a discontinuous function.

TL;DR: A spectral boundary integral method for simulating large numbers of blood cells flowing in complex geometries is developed and demonstrated and is shown to reproduce the well-known non-monotonic dependence of the effective viscosity on the tube diameter.

TL;DR: This paper focuses on examples from atomization simulations using the refined level set grid method, which is applicable to level set, Volume of Fluid, and marker particle interface tracking methods for the fully resolved scale.

TL;DR: This paper shows how to achieve a full and strong coupling between anisotropic mesh adaptation and goal-oriented error estimate in three steps based on a careful analysis of the contributions of the implicit error and of the interpolation error.

TL;DR: A novel finite-volume interface (contact) capturing method is presented for simulation of multi-component compressible flows with high density ratios and strong shocks, which employs Cartesian product stencils and, therefore, there is no inherent obstacles in multiple dimensions.

TL;DR: The numerical results indicate that this reconstruction-based discontinuous Galerkin (RDG) method is able to deliver the same accuracy as the well-known Bassi-Rebay II scheme, at a half of its computing costs for the discretization of the viscous fluxes in the Navier-Stokes equations, clearly demonstrating its superior performance over the existing DG methods.

TL;DR: A robust and efficient second order accurate numerical scheme for two and three-dimensional Euler and MHD flows is presented, built on the current multidimensional Riemann solver and implemented in the author's RIEMANN code.

TL;DR: A higher-order, state-based artificial viscosity with an associated governing partial differential equation (PDE) is proposed, which is less susceptible to errors introduced by grid edges oblique to captured shocks and boundary layers, thereby enabling accurate heat transfer predictions.

TL;DR: A theoretical framework is proposed to clearly explain the inaccuracy of Godunov type schemes applied to the compressible Euler system at low Mach number on a Cartesian mesh and to define a large class of colocated schemes accurate at lowMach number on any mesh.