A relaxation scheme for the hydrodynamic equations for semiconductors
Applied Numerical Mathematics
TVD Fluxes for the High-Order ADER Schemes
Journal of Scientific Computing
An adaptive local deconvolution method for implicit LES
Journal of Computational Physics
Numerical approximation of the viscous quantum hydrodynamic model for semiconductors
Applied Numerical Mathematics
MUSTA: a multi-stage numerical flux
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
Direct-expansion forms of ADER schemes for conservation laws and their verification
Journal of Computational Physics
δ-mapping algorithm coupled with WENO reconstruction for nonlinear elasticity in heterogeneous media
Applied Numerical Mathematics
ACM Transactions on Graphics (TOG)
ADER schemes for the shallow water equations in channel with irregular bottom elevation
Journal of Computational Physics
Asymptotic and numerical analysis of an inviscid bounded vortex flow at low Mach number
Journal of Computational Physics
Level Set Equations on Surfaces via the Closest Point Method
Journal of Scientific Computing
Characteristic-Based Schemes for Multi-Class Lighthill-Whitham-Richards Traffic Models
Journal of Scientific Computing
Journal of Computational Physics
Journal of Computational Physics
High order multi-moment constrained finite volume method. Part I: Basic formulation
Journal of Computational Physics
Journal of Computational Physics
Shock Capturing Artificial Dissipation for High-Order Finite Difference Schemes
Journal of Scientific Computing
Approximate solution of hyperbolic conservation laws by discrete mollification
Applied Numerical Mathematics
A massively parallel multi-block hybrid compact-WENO scheme for compressible flows
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
High-order conservative finite difference GLM-MHD schemes for cell-centered MHD
Journal of Computational Physics
Large eddy simulation using a new set of sixth order schemes for compressible viscous terms
Journal of Computational Physics
Detail-preserving fully-Eulerian interface tracking framework
ACM SIGGRAPH Asia 2010 papers
Journal of Computational Physics
Numerical study on propagation of explosion wave in h2-o2 mixtures
ICNC'06 Proceedings of the Second international conference on Advances in Natural Computation - Volume Part II
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Applications of level set methods in computational biophysics
Mathematical and Computer Modelling: An International Journal
Hybrid Well-balanced WENO Schemes with Different Indicators for Shallow Water Equations
Journal of Scientific Computing
Eulerian adaptive finite-difference method for high-velocity impact and penetration problems
Journal of Computational Physics
Block-structured adaptive mesh refinement algorithms for Vlasov simulation
Journal of Computational Physics
Accuracy of the weighted essentially non-oscillatory conservative finite difference schemes
Journal of Computational Physics
A HLL-Rankine-Hugoniot Riemann solver for complex non-linear hyperbolic problems
Journal of Computational Physics
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In these lecture notes we describe the construction, analysis, and application of ENO (Essentially Non-Oscillatory) and WENO (Weighted Essentially Non-Oscillatory) schemes for hyperbolic conservation laws and related Hamilton-Jacobi equations. ENO and WENO schemes are high order accurate finite difference schemes designed for problems with piecewise smooth solutions containing discontinuities. The key idea lies at the approximation level, where a nonlinear adaptive procedure is used to automatically choose the locally smoothest stencil, hence avoiding crossing discontinuities in the interpolation procedure as much as possible. ENO and WENO schemes have been quite successful in applications, especially for problems containing both shocks and complicated smooth solution structures, such as compressible turbulence simulations and aeroacoustics. These lecture notes are basically self-contained. It is our hope that with these notes and with the help of the quoted references, the reader can understand the algorithms and code them up for applications. Sample codes are also available from the author.