Shock-capturing and front-tracking methods for granular avalanches
Journal of Computational Physics
A smoothness indicator for adaptive algorithms for hyperbolic systems
Journal of Computational Physics
Journal of Computational Physics
High-order semi-discrete central-upwind schemes for multi-dimensional Hamilton--Jacobi equations
Journal of Computational Physics
Journal of Computational Physics
A central-constrained transport scheme for ideal magnetohydrodynamics
Journal of Computational Physics
Non-oscillatory central schemes for one- and two-dimensional MHD equations: I
Journal of Computational Physics
Variants of relaxed schemes and two-dimensional gas dynamics
Journal of Computational and Applied Mathematics - Special issue: Selected papers of the international conference on computational methods in sciences and engineering (ICCMSE-2003)
Adaptive Central-Upwind Schemes for Hamilton---Jacobi Equations with Nonconvex Hamiltonians
Journal of Scientific Computing
Staggered Finite Difference Schemes for Conservation Laws
Journal of Scientific Computing
On the Total Variation of High-Order Semi-Discrete Central Schemes for Conservation Laws
Journal of Scientific Computing
Finite-Volume-Particle Methods for Models of Transport of Pollutant in Shallow Water
Journal of Scientific Computing
Computations of steady and unsteady transport of pollutant in shallow water
Mathematics and Computers in Simulation
Applied Numerical Mathematics
Applied Numerical Mathematics - Numerical methods for viscosity solutions and applications
On a practical implementation of particle methods
Applied Numerical Mathematics - Selected papers from the first Chilean workshop on numerical analysis of partial differential equations (WONAPDE 2004)
Fourth-order balanced source term treatment in central WENO schemes for shallow water equations
Journal of Computational Physics
Explicit solutions to a convection-reaction equation and defects of numerical schemes
Journal of Computational Physics
Well-balanced finite volume evolution Galerkin methods for the shallow water equations
Journal of Computational Physics
Applied Numerical Mathematics
Journal of Computational Physics
Numerical solutions to a two-dimensional Riemann problem for gas dynamics equations
MATH'07 Proceedings of the 11th WSEAS International Conference on Applied Mathematics
A new fourth-order non-oscillatory central scheme for hyperbolic conservation laws
Applied Numerical Mathematics
Journal of Computational Physics
An efficient ghost fluid method for compressible multifluids in Lagrangian coordinate
Applied Numerical Mathematics
On the numerical solution of a driven thin film equation
Journal of Computational Physics
Non-oscillatory central-upwind scheme for hyperbolic conservation laws
International Journal of Computational Fluid Dynamics
Numerical Solution of a Two-Class LWR Traffic Flow Model by High-Resolution Central-Upwind Scheme
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part I: ICCS 2007
Discontinuous Galerkin methods for the chemotaxis and haptotaxis models
Journal of Computational and Applied Mathematics
A central conservative scheme for general rectangular grids
Journal of Computational Physics
A Second Order Central Scheme for Hamilton-Jacobi Equations on Triangular Grids
Numerical Analysis and Its Applications
Journal of Scientific Computing
POD-based feedback control of the burgers equation by solving the evolutionary HJB equation
Computers & Mathematics with Applications
Variants of relaxed schemes and two-dimensional gas dynamics
Journal of Computational and Applied Mathematics - Special issue: Selected papers of the international conference on computational methods in sciences and engineering (ICCMSE-2003)
Upwind-biased FORCE schemes with applications to free-surface shallow flows
Journal of Computational Physics
A Central Discontinuous Galerkin Method for Hamilton-Jacobi Equations
Journal of Scientific Computing
A Fast Explicit Operator Splitting Method for Passive Scalar Advection
Journal of Scientific Computing
A quasi-one-dimensional Riemann problem for the isentropic gas dynamics equations
MACMESE'07 Proceedings of the 9th WSEAS international conference on Mathematical and computational methods in science and engineering
Solving the euler equations on graphics processing units
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part IV
Mathematical and Computer Modelling: An International Journal
Computer modelling of haematopoietic stem cells migration
Computers & Mathematics with Applications
A Semidiscrete Finite Volume Constrained Transport Method on Orthogonal Curvilinear Grids
SIAM Journal on Scientific Computing
Alternating Evolution Schemes for Hyperbolic Conservation Laws
SIAM Journal on Scientific Computing
Original Article: High order well-balanced scheme for river flow modeling
Mathematics and Computers in Simulation
New adaptive artificial viscosity method for hyperbolic systems of conservation laws
Journal of Computational Physics
Journal of Scientific Computing
The Journal of Supercomputing
Mathematics and Computers in Simulation
Alternating evolution discontinuous Galerkin methods for Hamilton-Jacobi equations
Journal of Computational Physics
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We introduce new Godunov-type semidiscrete central schemes for hyperbolic systems of conservation laws and Hamilton--Jacobi equations. The schemes are based on the use of more precise information about the local speeds of propagation and can be viewed as a generalization of the schemes from [A. Kurganov and E. Tadmor, J. Comput. Phys., 160 (2000), pp. 241--282; A. Kurganov and D. Levy, SIAM J. Sci. Comput., 22 (2000), pp. 1461--1488; A. Kurganov and G. Petrova, A third-order semidiscrete genuinely multidimensional central scheme for hyperbolic conservation laws and related problems, Numer. Math., to appear] and [A. Kurganov and E. Tadmor, J. Comput. Phys., 160 (2000), pp. 720--742]. The main advantages of the proposed central schemes are the high resolution, due to the smaller amount of the numerical dissipation, and the simplicity. There are no Riemann solvers and characteristic decomposition involved, and this makes them a universal tool for a wide variety of applications.At the same time, the developed schemes have an upwind nature, since they respect the directions of wave propagation by measuring the one-sided local speeds. This is why we call them central-upwind schemes.The constructed schemes are applied to various problems, such as the Euler equations of gas dynamics, the Hamilton--Jacobi equations with convex and nonconvex Hamiltonians, and the incompressible Euler and Navier--Stokes equations. The incompressibility condition in the latter equations allows us to treat them both in their conservative and transport form. We apply to these problems the central-upwind schemes, developed separately for each of them, and compute the corresponding numerical solutions.