Computer Methods in Applied Mechanics and Engineering
Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Non-oscillatory central differencing for hyperbolic conservation laws
Journal of Computational Physics
Classification of the Riemann problem for two-dimensional gas dynamics
SIAM Journal on Mathematical Analysis
Numerical solution of the Riemann problem for two-dimensional gas dynamics
SIAM Journal on Scientific Computing
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
High resolution schemes for hyperbolic conservation laws
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
Formulations of artificial viscosity for multi-dimensional shock wave computations
Journal of Computational Physics
Journal of Computational Physics
A technique of treating negative weights in WENO schemes
Journal of Computational Physics
A smoothness indicator for adaptive algorithms for hyperbolic systems
Journal of Computational Physics
Compact Central WENO Schemes for Multidimensional Conservation Laws
SIAM Journal on Scientific Computing
Semidiscrete Central-Upwind Schemes for Hyperbolic Conservation Laws and Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
Adaptive Discontinuous Galerkin Finite Element Methods for Nonlinear Hyperbolic Conservation Laws
SIAM Journal on Scientific Computing
Adaptive discontinuous Galerkin finite element methods for the compressible Euler equations
Journal of Computational Physics
Power ENO methods: a fifth-order accurate weighted power ENO method
Journal of Computational Physics
Adaptive Semidiscrete Central-Upwind Schemes for Nonconvex Hyperbolic Conservation Laws
SIAM Journal on Scientific Computing
Journal of Computational Physics
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We propose a new finite volume method for solving general multidimensional hyperbolic systems of conservation laws. Our method is based on an appropriate numerical flux and a high-order piecewise polynomial reconstruction. The latter is utilized without any computationally expensive nonlinear limiters, which are typically needed to guarantee nonlinear stability of the scheme. Instead, we enforce stability of the proposed method by adding a new adaptive artificial viscosity, whose coefficients are proportional to the size of the weak local residual, which is sufficiently large (~@D, where @D is a discrete small scale) at the shock regions, much smaller (~@D^@a, where @a is close to 2) near the contact waves, and very small (~@D^4) in the smooth parts of the computed solution. We test the proposed scheme on a number of benchmarks for both scalar conservation laws and for one- and two-dimensional Euler equations of gas dynamics. The obtained numerical results clearly demonstrate the robustness and high accuracy of the new method.