Search results for "shock-capturing"

Hits ?▲	Authors	Title	Venue	Year	Link	Author keywords
87	Audrey Rault, Guillaume Chiavassa, Rosa Donat	Shock-Vortex Interactions at High Mach Numbers.	J. Sci. Comput.	2003	DBLP DOI BibTeX RDF	shock capturing schemes, composite vortex, shock deformation
79	H. C. Yee 0001, Björn Sjögreen	Non-Linear Filtering and Limiting in High Order Methods for Ideal and Non-Ideal MHD.	J. Sci. Comput.	2006	DBLP DOI BibTeX RDF	High order schemes filtering, MHD, shock-capturing, shock/turbulence interactions, nonlinear filtering, limiting
64	Ellen M. Taylor, M. Pino Martín	Stencil Adaptation Properties of a WENO Scheme in Direct Numerical Simulations of Compressible Turbulence.	J. Sci. Comput.	2007	DBLP DOI BibTeX RDF	Shock capturing, adaptive numerical method, WENO, compressible turbulence, isotropic turbulence, DNS
56	Appanah Rao Appadu, Muhammad Zaid Dauhoo, S. D. D. V. Rughooputh	Efficient Shock-Capturing Numerical Schemes Using the Approach of Minimised Integrated Square Difference Error for Hyperbolic Conservation Laws.	ICCSA (3)	2007	DBLP DOI BibTeX RDF	4-6 Low-Dissipation and Dispersion Runge Kutta, LW????, Minimised Integrated Square Difference Error
53	Rosa Donat, Pep Mulet	Characteristic-Based Schemes for Multi-Class Lighthill-Whitham-Richards Traffic Models.	J. Sci. Comput.	2008	DBLP DOI BibTeX RDF	Multi-class Lighthill Whitham Richards traffic model, High resolution shock capturing schemes, Finite-difference WENO schemes, Adaptive mesh refinement
53	H. C. Yee 0001, Björn Sjögreen	Efficient Low Dissipative High Order Schemes for Multiscale MHD Flows, II: Minimization of Delta*B Numerical Error.	J. Sci. Comput.	2006	DBLP DOI BibTeX RDF	Magnetohydrodynamics, difference scheme, high order of accuracy, shock capturing, numerical divergence
51	Renato Paciorri, Aldo Bonfiglioli	Accurate detection of shock waves and shock interactions in two-dimensional shock-capturing solutions.	J. Comput. Phys.	2020	DBLP DOI BibTeX RDF
40	Emad Fatemi, Joseph W. Jerome, Stanley J. Osher	Solution of the hydrodynamic device model using high-order nonoscillatory shock capturing algorithms.	IEEE Trans. Comput. Aided Des. Integr. Circuits Syst.	1991	DBLP DOI BibTeX RDF
39	Shujun Fu, Qiuqi Ruan, Chengpo Mu, Wenqia Wang	Geometry-Driven Nonlinear Equation with an Accelerating Coupled Scheme for Image Enhancement.	International Conference on Computational Science (1)	2007	DBLP DOI BibTeX RDF
39	Shujun Fu, Qiuqi Ruan, Wenqia Wang, Jingnian Chen	Region-Based Shock-Diffusion Equation for Adaptive Image Enhancement.	IWICPAS	2006	DBLP DOI BibTeX RDF
39	Shujun Fu, Qiuqi Ruan, Wenqia Wang, Jingnian Chen	Feature-Oriented Fuzzy Shock-Diffusion Equation for Adaptive Image Resolution Enhancement.	FSKD	2006	DBLP DOI BibTeX RDF
39	Björn Sjögreen, H. C. Yee 0001	Multiresolution Wavelet Based Adaptive Numerical Dissipation Control for High Order Methods.	J. Sci. Comput.	2004	DBLP DOI BibTeX RDF	low dissipation, high order finite difference method, TVD schemes, wavelets, multi resolution, shock waves
37	Renato Paciorri, Aldo Bonfiglioli	Recognition of shock-wave patterns from shock-capturing solutions.	CompIMAGE	2012	DBLP DOI BibTeX RDF
37	Michael Breuß, Thomas Brox, Thomas Sonar, Joachim Weickert	Stabilised Nonlinear Inverse Diffusion for Approximating Hyperbolic PDEs.	Scale-Space	2005	DBLP DOI BibTeX RDF
37	Xing He, Ann R. Karagozian	Numerical Simulation of Pulse Detonation Engine Phenomena.	J. Sci. Comput.	2003	DBLP DOI BibTeX RDF	detonations, gasdynamics, reactive Euler equations, shock capturing schemes
37	Huanan Yang	A Local Extrapolation Method for Hyperbolic Conservation Laws. I. The ENO Underlying Schemes.	J. Sci. Comput.	2000	DBLP DOI BibTeX RDF	shock capturing schemes, extrapolation method, conservation law
26	John Steinhoff, Meng Fan, Lesong Wang, William Dietz	Convection of Concentrated Vortices and Passive Scalars as Solitary Waves.	J. Sci. Comput.	2003	DBLP DOI BibTeX RDF	vortical flow, scalar convection, solitary wave, vorticity confinement, CFD
24	Sai Swetha Venkata Kolluru, Nicolas Besse, Rahul Pandit	Novel spectral methods for shock capturing and the removal of tygers in computational fluid dynamics.	CoRR	2024	DBLP DOI BibTeX RDF
24	Weijie Ren, Wenjia Xie, Ye Zhang, Hang Yu, Zhengyu Tian	MSAT: Matrix stability analysis tool for shock-capturing schemes.	SoftwareX	2023	DBLP DOI BibTeX RDF
24	Yaming Chen, Xiaogang Deng	Nonlinear weights for shock capturing schemes with unconditionally optimal high order.	J. Comput. Phys.	2023	DBLP DOI BibTeX RDF
24	S. R. Siva Prasad Kochi, M. Ramakrishna 0001	Shock capturing using discontinuous Galerkin method and overset grids for two-dimensional Euler equations.	J. Comput. Phys.	2023	DBLP DOI BibTeX RDF
24	Fengrui Zhang, Yulia T. Peet	Discontinuous Galerkin spectral element method for shock capturing with summation by parts properties.	J. Comput. Phys. X	2023	DBLP DOI BibTeX RDF
24	Weijie Ren, Wenjia Xie, Ye Zhang, Hang Yu, Zhengyu Tian	Numerical stability analysis of shock-capturing methods for strong shocks I: second-order MUSCL schemes.	CoRR	2023	DBLP DOI BibTeX RDF
24	Ngoc Cuong Nguyen, R. Loek Van Heyningen, Jordi Vila-Pérez, Jaime Peraire	Optimal transport for mesh adaptivity and shock capturing of compressible flows.	CoRR	2023	DBLP DOI BibTeX RDF
24	Shaoshuai Chu, Olyana A. Kovyrkina, Alexander Kurganov, Vladimir V. Ostapenko	Experimental Convergence Rate Study for Three Shock-Capturing Schemes and Development of Highly Accurate Combined Schemes.	CoRR	2023	DBLP DOI BibTeX RDF
24	Andrés Mateo-Gabín, Kenza Tlales, Eusebio Valero, Esteban Ferrer, Gonzalo Rubio	Unsupervised machine-learning shock-capturing technique for high-order solvers.	CoRR	2023	DBLP DOI BibTeX RDF
24	Weijie Ren, Wenjia Xie, Ye Zhang, Hang Yu, Zhengyu Tian	MSAT: Matrix stability analysis tool for shock-capturing schemes.	CoRR	2023	DBLP DOI BibTeX RDF
24	Weijie Ren, Wenjia Xie, Ye Zhang, Hang Yu, Zhengyu Tian	Numerical stability analysis of shock-capturing methods for strong shocks II: high-order finite-volume schemes.	CoRR	2023	DBLP DOI BibTeX RDF
24	Victor C. B. Sousa, Carlo Scalo	Corrigendum to "A unified Quasi-Spectral Viscosity (QSV) approach to shock capturing and large-eddy simulation" [J. Comput. Phys. 455 (2022) 111139].	J. Comput. Phys.	2022	DBLP DOI BibTeX RDF
24	Victor C. B. Sousa, Carlo Scalo	A Legendre spectral viscosity (LSV) method applied to shock capturing for high-order flux reconstruction schemes.	J. Comput. Phys.	2022	DBLP DOI BibTeX RDF
24	Victor C. B. Sousa, Carlo Scalo	A unified Quasi-Spectral Viscosity (QSV) approach to shock capturing and large-eddy simulation.	J. Comput. Phys.	2022	DBLP DOI BibTeX RDF
24	Andrés Mateo-Gabín, Juan Manzanero, Eusebio Valero	An entropy stable spectral vanishing viscosity for discontinuous Galerkin schemes: Application to shock capturing and LES models.	J. Comput. Phys.	2022	DBLP DOI BibTeX RDF
24	C. R. Jisha, T. K. Riyasudheen, Ritesh Kumar Dubey	A novel numerical viscosity for fourth order hybrid entropy stable shock capturing schemes for convection diffusion equation.	J. Comput. Phys.	2022	DBLP DOI BibTeX RDF
24	Per-Olof Persson, Benjamin Stamm	A discontinuous Galerkin method for shock capturing using a mixed high-order and sub-grid low-order approximation space.	J. Comput. Phys.	2022	DBLP DOI BibTeX RDF
24	Pascal Mossier, Andrea Beck, Claus-Dieter Munz	A p-Adaptive Discontinuous Galerkin Method with hp-Shock Capturing.	J. Sci. Comput.	2022	DBLP DOI BibTeX RDF
24	Sebastian Hennemann, Andrés M. Rueda-Ramírez, Florian J. Hindenlang, Gregor J. Gassner	A provably entropy stable subcell shock capturing approach for high order split form DG for the compressible Euler equations.	J. Comput. Phys.	2021	DBLP DOI BibTeX RDF
24	Yue Li, Lin Fu, Nikolaus A. Adams	A low-dissipation shock-capturing framework with flexible nonlinear dissipation control.	J. Comput. Phys.	2021	DBLP DOI BibTeX RDF
24	Amareshwara Sainadh Chamarthi, Steven H. Frankel	High-order central-upwind shock capturing scheme using a Boundary Variation Diminishing (BVD) algorithm.	J. Comput. Phys.	2021	DBLP DOI BibTeX RDF
24	Andrés M. Rueda-Ramírez, Sebastian Hennemann, Florian J. Hindenlang, Andrew R. Winters, Gregor J. Gassner	An entropy stable nodal discontinuous Galerkin method for the resistive MHD equations. Part II: Subcell finite volume shock capturing.	J. Comput. Phys.	2021	DBLP DOI BibTeX RDF
24	Huaibao Zhang, Fan Zhang	On the numerical overshoots of shock-capturing schemes.	CoRR	2021	DBLP BibTeX RDF
24	Andrés Mateo-Gabín, Juan Manzanero, Eusebio Valero	An entropy stable spectral vanishing viscosity for discontinuous Galerkin schemes: application to shock capturing and LES models.	CoRR	2021	DBLP BibTeX RDF
24	Huajun Zhu, Huayong Liu, Zhen-Guo Yan, Guoquan Shi, Xiaogang Deng	Shock capturing schemes based on nonuniform nonlinear weighted interpolation for conservation laws and their application as subcell limiters for FR/CPR.	CoRR	2021	DBLP BibTeX RDF
24	Tatiana Kossaczká, Matthias Ehrhardt 0001, Michael Günther 0005	Enhanced fifth order WENO Shock-Capturing Schemes with Deep Learning.	CoRR	2021	DBLP BibTeX RDF
24	Tarik Dzanic, Will Trojak, Freddie D. Witherden	Utilizing Time-Reversibility for Shock Capturing in Nonlinear Hyperbolic Conservation Laws.	CoRR	2021	DBLP BibTeX RDF
24	Eduardo Abreu, Vítor Matos, John Pérez, P. Rodríguez-Bermúdez	A Class of Lagrangian-Eulerian Shock-Capturing Schemes for First-Order Hyperbolic Problems with Forcing Terms.	J. Sci. Comput.	2021	DBLP DOI BibTeX RDF
24	Takahiro Miyoshi, Takashi Minoshima	A short note on reconstruction variables in shock capturing schemes for magnetohydrodynamics.	J. Comput. Phys.	2020	DBLP DOI BibTeX RDF
24	Tarik Dzanic, Will Trojak, Freddie D. Witherden	A Riemann Difference Scheme for Shock Capturing in Discontinuous Finite Element Methods.	CoRR	2020	DBLP BibTeX RDF
24	Andrés M. Rueda-Ramírez, Sebastian Hennemann, Florian J. Hindenlang, Andrew R. Winters, Gregor Gassner	An Entropy Stable Nodal Discontinuous Galerkin Method for the resistive MHD Equations. Part II: Subcell Finite Volume Shock Capturing.	CoRR	2020	DBLP BibTeX RDF
24	Ben Stevens, Tim Colonius	Enhancement of shock-capturing methods via machine learning.	CoRR	2020	DBLP BibTeX RDF
24	Amareshwara Sainadh Chamarthi, Steven H. Frankel	High-Order Central-Upwind shock capturing scheme using a Boundary Variation Diminishing (BVD) Algorithm.	CoRR	2020	DBLP BibTeX RDF
24	S. R. Siva Prasad Kochi, M. Ramakrishna 0001	Shock capturing with discontinuous Galerkin Method using Overset grids for two-dimensional Euler equations.	CoRR	2020	DBLP BibTeX RDF
24	Yue Li, Lin Fu, Nikolaus A. Adams	A low-dissipation shock-capturing framework with flexible nonlinear dissipation control.	CoRR	2020	DBLP BibTeX RDF
24	Johannes Markert, Gregor Gassner, Stefanie Walch	A Sub-Element Adaptive Shock Capturing Approach for Discontinuous Galerkin Methods.	CoRR	2020	DBLP BibTeX RDF
24	Lin Fu	A low-dissipation finite-volume method based on a new TENO shock-capturing scheme.	Comput. Phys. Commun.	2019	DBLP DOI BibTeX RDF
24	Jan Glaubitz	Shock capturing by Bernstein polynomials for scalar conservation laws.	Appl. Math. Comput.	2019	DBLP DOI BibTeX RDF
24	Stavros Avgerinos, Florian Bernard, Angelo Iollo, Giovanni Russo 0001	Linearly implicit all Mach number shock capturing schemes for the Euler equations.	J. Comput. Phys.	2019	DBLP DOI BibTeX RDF
24	Xi Deng, Yuya Shimizu, Feng Xiao 0001	A fifth-order shock capturing scheme with two-stage boundary variation diminishing algorithm.	J. Comput. Phys.	2019	DBLP DOI BibTeX RDF
24	Guoyan Zhao 0003, Mingbo Sun, Antonio Memmolo, Sergio Pirozzoli	A general framework for the evaluation of shock-capturing schemes.	J. Comput. Phys.	2019	DBLP DOI BibTeX RDF
24	Eric J. Ching, Yu Lv, Peter A. Gnoffo, Michael Barnhardt, Matthias Ihme	Shock capturing for discontinuous Galerkin methods with application to predicting heat transfer in hypersonic flows.	J. Comput. Phys.	2019	DBLP DOI BibTeX RDF
24	Adam Reyes, Dongwook Lee 0004, Carlo Graziani, Petros Tzeferacos	A variable high-order shock-capturing finite difference method with GP-WENO.	J. Comput. Phys.	2019	DBLP DOI BibTeX RDF
24	Per-Olof Persson, Benjamin Stamm	A Discontinuous Galerkin method for Shock Capturing using a mixed high-order and sub-grid low-order approximation space.	CoRR	2019	DBLP BibTeX RDF
24	Marvin Bohm, Sven Schermeng, Andrew R. Winters, Gregor J. Gassner, Gustaaf B. Jacobs	Multi-element SIAC filter for shock capturing applied to high-order discontinuous Galerkin spectral element methods.	CoRR	2019	DBLP BibTeX RDF
24	Jan Glaubitz	Shock Capturing by Bernstein Polynomials for Scalar Conservation Laws.	CoRR	2019	DBLP BibTeX RDF
24	Jan Glaubitz, Alberto Costa Nogueira Jr., João Lucas de Sousa Almeida, R. F. Cantão, C. A. C. Silva	Smooth and Compactly Supported Viscous Sub-cell Shock Capturing for Discontinuous Galerkin Methods.	J. Sci. Comput.	2019	DBLP DOI BibTeX RDF
24	Marvin Bohm, Sven Schermeng, Andrew R. Winters, Gregor J. Gassner, Gustaaf B. Jacobs	Multi-element SIAC Filter for Shock Capturing Applied to High-Order Discontinuous Galerkin Spectral Element Methods.	J. Sci. Comput.	2019	DBLP DOI BibTeX RDF
24	Mehdi Mollaei, Seyyed Majid Malek Jafarian	The introduction of the surfing scheme for shock capturing with high-stability and high-speed convergence.	Commun. Nonlinear Sci. Numer. Simul.	2019	DBLP DOI BibTeX RDF
24	Taku Ohwada, Yuki Shibata, Takuma Kato, Taichi Nakamura	A simple, robust and efficient high-order accurate shock-capturing scheme for compressible flows: Towards minimalism.	J. Comput. Phys.	2018	DBLP DOI BibTeX RDF
24	D. V. Kotov, H. C. Yee 0001, A. A. Wray, Björn Sjögreen, Alexei G. Kritsuk	Corrigendum to "Numerical dissipation control in high order shock-capturing schemes for LES of low speed flows" [J. Comput. Phys. 307 (2016) 189-202].	J. Comput. Phys.	2018	DBLP DOI BibTeX RDF
24	David Sidilkover	Towards unification of the Vorticity Confinement and Shock Capturing (TVD and ENO/WENO) methods.	J. Comput. Phys.	2018	DBLP DOI BibTeX RDF
24	Frédéric Coquel, Shi Jin 0003, Jian-Guo Liu 0006, Li Wang 0020	Entropic sub-cell shock capturing schemes via Jin-Xin relaxation and Glimm front sampling for scalar conservation laws.	Math. Comput.	2018	DBLP DOI BibTeX RDF
24	Carlos Pantano, Richard Saurel, T. Schmitt	An oscillation free shock-capturing method for compressible van der Waals supercritical fluid flows.	J. Comput. Phys.	2017	DBLP DOI BibTeX RDF
24	Sergio Amat, Vicente F. Candela	On the convergence of a local third order shock capturing method for hyperbolic conservation laws.	Numer. Algorithms	2017	DBLP DOI BibTeX RDF
24	Matthias Sonntag, Claus-Dieter Munz	Efficient Parallelization of a Shock Capturing for Discontinuous Galerkin Methods using Finite Volume Sub-cells.	J. Sci. Comput.	2017	DBLP DOI BibTeX RDF
24	Mohammad Zakerzadeh, Georg May	On the Convergence of a Shock Capturing Discontinuous Galerkin Method for Nonlinear Hyperbolic Systems of Conservation Laws.	SIAM J. Numer. Anal.	2016	DBLP DOI BibTeX RDF
24	D. V. Kotov, H. C. Yee 0001, A. A. Wray, Björn Sjögreen, Alexei G. Kritsuk	Numerical dissipation control in high order shock-capturing schemes for LES of low speed flows.	J. Comput. Phys.	2016	DBLP DOI BibTeX RDF
24	Vladimir V. Ostapenko, Olyana Kovyrkina	On Construction of Combined Shock-Capturing Finite-Difference Schemes of High Accuracy.	NAA	2016	DBLP DOI BibTeX RDF
24	Forrest Wolfgang Glines, Matthew Anderson, David Neilsen	Scalable Relativistic High-Resolution Shock-Capturing for Heterogeneous Computing.	CLUSTER	2015	DBLP DOI BibTeX RDF
24	Andreas Hiltebrand, Siddhartha Mishra	Entropy stable shock capturing space-time discontinuous Galerkin schemes for systems of conservation laws.	Numerische Mathematik	2014	DBLP DOI BibTeX RDF
24	Hamdullah Yücel, Martin Stoll, Peter Benner	Discontinuous Galerkin finite element methods with shock-capturing for nonlinear convection dominated models.	Comput. Chem. Eng.	2013	DBLP DOI BibTeX RDF
24	H. C. Yee 0001, D. V. Kotov, Wei Wang 0027, Chi-Wang Shu	Spurious behavior of shock-capturing methods by the fractional step approach: Problems containing stiff source terms and discontinuities.	J. Comput. Phys.	2013	DBLP DOI BibTeX RDF
24	Andrew W. Cook	Effects of heat conduction on artificial viscosity methods for shock capturing.	J. Comput. Phys.	2013	DBLP DOI BibTeX RDF
24	H. C. Yee 0001, D. V. Kotov, Wei Wang 0027, Chi-Wang Shu	Corrigendum to "Spurious behavior of shock-capturing methods by the fractional step approach: Problems containing stiff source terms and discontinuities" [J. Comput. Physics 241 (2013) 266-291].	J. Comput. Phys.	2013	DBLP DOI BibTeX RDF
24	J. R. Serrano, H. Climent, Pedro Piqueras, Oscar García-Afonso	Analysis of shock capturing methods for chemical species transport in unsteady compressible flow.	Math. Comput. Model.	2013	DBLP DOI BibTeX RDF
24	Friedhelm Schieweck, Piotr Skrzypacz	A Local Projection Stabilization Method with Shock Capturing and Diagonal Mass Matrix for Solving Non-stationary Transport Dominated Problems.	Comput. Methods Appl. Math.	2012	DBLP DOI BibTeX RDF
24	Appanah Rao Appadu	Investigating the shock-capturing properties of some composite numerical schemes for the 1-D linear advection equation.	Int. J. Comput. Appl. Technol.	2012	DBLP DOI BibTeX RDF
24	Garrett E. Barter, David L. Darmofal	Shock capturing with PDE-based artificial viscosity for DGFEM: Part I. Formulation.	J. Comput. Phys.	2010	DBLP DOI BibTeX RDF
24	Olivier Heuzé, Stéphane Jaouen, Hervé Jourdren	Dissipative issue of high-order shock capturing schemes with non-convex equations of state.	J. Comput. Phys.	2009	DBLP DOI BibTeX RDF
24	Christophe Bogey, Nicolas de Cacqueray, Christophe Bailly	A shock-capturing methodology based on adaptative spatial filtering for high-order non-linear computations.	J. Comput. Phys.	2009	DBLP DOI BibTeX RDF
24	Magnus Svärd, Siddhartha Mishra	Shock Capturing Artificial Dissipation for High-Order Finite Difference Schemes.	J. Sci. Comput.	2009	DBLP DOI BibTeX RDF
24	Ritesh Kumar, Mohan K. Kadalbajoo	A class of high resolution shock capturing schemes for hyperbolic conservation laws.	Appl. Math. Comput.	2008	DBLP DOI BibTeX RDF
24	S. Kudriakov, W. H. Hui	On a new defect of shock-capturing methods.	J. Comput. Phys.	2008	DBLP DOI BibTeX RDF
24	Ben Thornber, Dimitris Drikakis, Robin J. R. Williams, David Youngs	On entropy generation and dissipation of kinetic energy in high-resolution shock-capturing schemes.	J. Comput. Phys.	2008	DBLP DOI BibTeX RDF
24	Zheng Ran	Lie Symmetry Preservation and Shock-Capturing Methods.	SIAM J. Numer. Anal.	2007	DBLP DOI BibTeX RDF
24	Guo-Hua Tu, Xiang-Jiang Yuan	A characteristic-based shock-capturing scheme for hyperbolic problems.	J. Comput. Phys.	2007	DBLP DOI BibTeX RDF
24	Leonardo Di G. Sigalotti, Hender López, Arnaldo Donoso, Eloy Sira, Jaime Klapp	A shock-capturing SPH scheme based on adaptive kernel estimation.	J. Comput. Phys.	2006	DBLP DOI BibTeX RDF
24	Sergio Pirozzoli	On the spectral properties of shock-capturing schemes.	J. Comput. Phys.	2006	DBLP DOI BibTeX RDF
24	Michael Breuß, Joachim Weickert	A Shock-Capturing Algorithm for the Differential Equations of Dilation and Erosion.	J. Math. Imaging Vis.	2006	DBLP DOI BibTeX RDF
24	Tsutomu Saito, Atsushi Abe, Kazuyoshi Takayama	Benchmark of Parallelization Methods for Unstructured Shock Capturing Code.	IPDPS	2001	DBLP DOI BibTeX RDF
24	Kaleem Siddiqi, Benjamin B. Kimia, Chi-Wang Shu	Geometric Shock-Capturing ENO Schemes for Subpixel Interpolation, Computation and Curve Evolution.	CVGIP Graph. Model. Image Process.	1997	DBLP DOI BibTeX RDF
16	Gabriella Puppo, Giovanni Russo 0001	Staggered Finite Difference Schemes for Conservation Laws.	J. Sci. Comput.	2006	DBLP DOI BibTeX RDF	balance laws, central schemes, Conservation laws, high-order accuracy, finite difference schemes