A space-time adaptive scheme is presented for solving advection equations in two space dimensions. The gradient-augmented level set method using a semi-Lagrangian formulation with backward time integration is coupled with a point value multiresolution analysis using Her-mite interpolation. Thus locally refined dyadic spatial grids are introduced which are efficiently implemented with dynamic qu...

In this work, we deal with the 1D compressible fluid coupled with elastic solid in an Eulerian-Lagrangian system. To facilitate the analysis, the Naviers equation for elastic solid is cast into a 2×2 system similar to the Euler equation but in Lagrangian coordinate. The modified Ghost Fluid Method is employed to treat the fluid-elastic solid coupling, where an Eulerian-Lagrangian Riemann proble...

The immersed boundary (IB) method is an approach to fluid-structure interaction that uses Lagrangian variables to describe the structure and Eulerian variables to describe the fluid. Explicit time stepping schemes for the IB method require solvers only for Eulerian equations, for which fast Cartesian grid solution methods are available. Such methods are relatively straightforward to develop and...

We present a numerical method for computing elasto-plastic ows in metals. The method uses a conservative Eulerian formulation of elasto-plasticity together with a higher-order Godunov nite diierence method combined with tracking of material boundaries. The Eulerian approach avoids the problem of mesh distortion caused by a Lagrangian remap, and can be easily extended to the computation of ows i...

The particle-in-cell method (PIC), especially the latest version of it, the material point method (MPM), has shown significant advantage over the pure Lagrangian method or the pure Eulerian method in numerical simulations of problems involving large deformations. It avoids the mesh distortion and tangling issues associated with Lagrangian methods and the advection errors associated with Euleria...

We develop some new variations of the Randomized Spectral Method (RSM) and Fourier-Wavelet Method (FWM) for the simulation of homogeneous Gaussian random vector fields based on plane wave decompositions. Some general conditions on the spectral density tensor of the random field which guarantee the theoretical convergence of the numerical representations are given. We then compare the various ra...

A hierarchical structure model is developed for anomalous scaling of the Lagrangian velocity structure functions in fully developed turbulence. This model is an extension of the Eulerian hierarchical structure model of She and Leveque [Phys. Rev. Lett. 72, 366 (1994)] to the Lagrangian velocity structure functions, where the straining and sweeping hypotheses are used to build up the relationshi...

The motion of a viscous incompressible fluid flow in bounded domains with a smooth boundary can be described by the nonlinear Navier-Stokes equations. This description corresponds to the so-called Eulerian approach. We develop a new approximation method for the Navier-Stokes equations in both the stationary and the non-stationary case by a suitable coupling of the Eulerian and the Lagrangian re...

We propose a new Eulerian-Lagrangian (EL) discontinuous Galerkin (DG) method formulated by introducing modified adjoint problem for the test function and performing integration of PDE over space-time region partitioned time-dependent linear functions approximating characteristics. The error incurred in characteristics approximation can then be taken into account flux term, integrated method-of-...