A 2D lattice Boltzmann model for inviscid compressible flows was proposed in this paper. Finite volume method was implemented on 2D curvilinear structural grids to solve the lattice BGK-Boltzmann equations. MUSCL scheme was used to perform interpolation. The obtained results agree excellently well with experimental and previous numerical results. AMS subject classifications: 76P05

Convergence of a second-order shock-capturing scheme for the system of isentropic gas dynamics with L°° initial data is established by analyzing the entropy dissipation measures. This scheme is modified from the classical MUSCL scheme to treat the vacuum problem in gas fluids and to capture local entropy near shock waves. Convergence of this scheme for the piston problem is also discussed.

We develop, implement and test a new third order accurate MUSCL type nite volume scheme for the two-dimensional Euler equations of com-pressible uid ow and compare the scheme with an anlogous second order scheme. It turns out that for many applications the third order scheme is less eecient than the second order one.

We present numerical comparisons for the simulation of unsteady 2D shallow water flows over topography with wet/dry fronts, between well-balanced cell-centered and node-centered formulations of a finite volume high-resolution algorithm. In both formulations we utilize Roe’s Riemann solver, while second-order spatial accuracy is achieved with MUSCL-type reconstruction techniques. Grid refinement...

When adopting high-order finite volume schemes based on MUSCL reconstruction techniques to approximate the weak solutions of hyperbolic systems with source terms, preservation steady states turns out be very challenging. Indeed, designed must preserve under consideration in order get required well-balancedness property. A priori, capture such a state, one needs solve some strongly nonlinear equ...

In this paper, we discuss the U-MUSCL reconstruction scheme -- an unstructured-grid extension of Van Leer's kappa-scheme proposed by Burg for edge-based discretization [AIAA Paper 2005-4999]. This technique has been widely used in practical fluid-dynamics solvers but with confusions: e.g., third-order accuracy kappa=1/2 or kappa=1/3. paper clarifies some these can be accurate point-valued solut...