AZTEC: a front tracking code based on Godunov's method
Applied Numerical Mathematics - Special issue in honor of Milt Rose's sixtieth birthday
Vorticity errors in multidimensional Lagrangian codes
Journal of Computational Physics
Computational methods in Lagrangian and Eulerian hydrocodes
Computer Methods in Applied Mechanics and Engineering
An arbitrary Lagrangian-Eulerian computing method for all flow speeds
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
Solution of Two-Dimensional Riemann Problems of Gas Dynamics by Positive Schemes
SIAM Journal on Scientific Computing
An r-adaptive finite element method based upon moving mesh PDEs
Journal of Computational Physics
A unified coordinate system for solving the two-dimensional Euler equations
Journal of Computational Physics
Computational Fluid Dynamics with Moving Boundaries
Computational Fluid Dynamics with Moving Boundaries
Journal of Computational Physics
Reference Jacobian optimization-based rezone strategies for arbitrary Lagrangian Eulerian methods
Journal of Computational Physics
A Moving Mesh Method for One-dimensional Hyperbolic Conservation Laws
SIAM Journal on Scientific Computing
Adaptive Mesh Methods for One- and Two-Dimensional Hyperbolic Conservation Laws
SIAM Journal on Numerical Analysis
Conservative Front Tracking with Improved Accuracy
SIAM Journal on Numerical Analysis
Runge--Kutta Discontinuous Galerkin Method Using WENO Limiters
SIAM Journal on Scientific Computing
Second-order Godunov-type scheme for reactive flow calculations on moving meshes
Journal of Computational Physics
An adaptive grid method for two-dimensional viscous flows
Journal of Computational Physics
A unified moving grid gas-kinetic method in Eulerian space for viscous flow computation
Journal of Computational Physics
A high order ENO conservative Lagrangian type scheme for the compressible Euler equations
Journal of Computational Physics
Efficient kinetic schemes for steady and unsteady flow simulations on unstructured meshes
Journal of Computational Physics
A DGBGK scheme based on WENO limiters for viscous and inviscid flows
Journal of Computational Physics
Journal of Scientific Computing
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Based on the integral form of the fluid dynamic equations, a finite volume kinetic scheme with arbitrary control volume and mesh velocity is developed. Different from the earlier unified moving mesh gas-kinetic method [C.Q. Jin, K. Xu, An unified moving grid gas-kinetic method in Eulerian space for viscous flow computation, J. Comput. Phys. 222 (2007) 155-175], the coupling of the fluid equations and geometrical conservation laws has been removed in order to make the scheme applicable for any quadrilateral or unstructured mesh rather than parallelogram in 2D case. Since a purely Lagrangian method is always associated with mesh entangling, in order to avoid computational collapsing in multidimensional flow simulation, the mesh velocity is constructed by considering both fluid velocity (Lagrangian methodology) and diffusive velocity (Regenerating Eulerian mesh function). Therefore, we obtain a generalized Arbitrary-Lagrangian-Eulerian (ALE) method by properly designing a mesh velocity instead of re-generating a new mesh after distortion. As a result, the remapping step to interpolate flow variables from old mesh to new mesh is avoided. The current method provides a general framework, which can be considered as a remapping-free ALE-type method. Since there is great freedom in choosing mesh velocity, in order to improve the accuracy and robustness of the method, the adaptive moving mesh method [H.Z. Tang, T. Tang, Adaptive mesh methods for one-and two-dimensional hyperbolic conservation laws, SIAM J. Numer. Anal. 41 (2003) 487-515] can be also used to construct a mesh velocity to concentrate mesh to regions with high flow gradients.