a fundamental topic in computational fluid dynamics is the role of coordinate particularly for searching optimized coordinates. the objective of this study is the numerical modeling of supersonic flows using a new coordinate system i.e. unified coordinate system (ucs) uses moving mesh with motionless viewing window technique. ucs has an advantage over traditional coordinate systems (eulerian an...

In this paper we present a novel technique for the simulation of moving boundaries and rigid bodies immersed in rarefied gas using an Eulerian-Lagrangian formulation based on least square method. The is simulated by solving Bhatnagar-Gross-Krook (BGK) model Boltzmann equation dynamics. BGK solved Arbitrary Lagrangian-Eulerian (ALE) method, where grid-points/particles are moved with mean velocit...

In this paper we first briefly review the semi-analytical method [20] for solving the Derivative Riemann Problem for systems of hyperbolic conservation laws with source terms. Next, we generalize it to hyperbolic systems for which the Riemann problem solution is not available. As an application example we implement the new derivative Riemann solver in the high-order finite-volume ADER advection...

Error was identified in Reference 1 subsequent to its publication. The citing [12] should read as2: Donea J, Huerta A, Ponthot J-Ph, Rodríguez-Ferran A. Arbitrary Lagrangian–Eulerian Methods, chapter 14. American Cancer Society, Atlanta, Georgia, 2004. Figure reference “Figure 3A” on page 818 (both) and 820, 1A”, be as, 2A. We apologize for this error.

In this paper, we consider the variable-order Galilei advection diffusion equation with a nonlinear source term. A numerical scheme with first order temporal accuracy and second order spatial accuracy is developed to simulate the equation. The stability and convergence of the numerical scheme are analyzed. Besides, another numerical scheme for improving temporal accuracy is also developed. Fina...

We study coherent structures in solar photospheric flows in a plage in the vicinity of the active region AR 10930 using the horizontal velocity data derived from Hinode/Solar Optical Telescope magnetograms. Eulerian and Lagrangian coherent structures (LCSs) are detected by computing the Q-criterion and the finite-time Lyapunov exponents of the velocity field, respectively. Our analysis indicate...

The objective of the Arbitrary Lagrangian-Eulerian (ALE) methodology for solving multidimensional fluid flow problems is to move the computational mesh, using the flow as a guide, to improve the robustness, accuracy and efficiency of a simulation. The main elements in the ALE simulation are an explicit Lagrangian phase, a rezone phase in which a new mesh is defined, and a remapping (conservativ...

The role of the Lagrangian mean flow, or drift, in modulating geometry, kinematics and dynamics rotational irrotational deep-water surface gravity waves is examined. A general theory for permanent progressive on an arbitrary vertically sheared steady flow derived reference frame mapped to Eulerian frame. viewpoint offers tremendous flexibility due particle labelling freedom allows us reveal how...

This paper introduces LEoPart, an add-on for the open source finite element software library FEniCS to seamlessly integrate Lagrangian particle functionality with (Eulerian) mesh-based (FE) approaches. LEoPart - which is so much as say: `Lagrangian-Eulerian on Particles' contains tools efficient, accurate and scalable advection of particles arbitrary polyhedral meshes. In addition, comes severa...

We perform a systematic multiscale analysis for the 2-D incompressible Euler equation with rapidly oscillating initial data using a Lagrangian approach. The Lagrangian formulation enables us to capture the propagation of the multiscale solution in a natural way. By making an appropriate multiscale expansion in the vorticity-stream function formulation, we derive a well-posed homogenized equatio...