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Nonoscillatory central differencing for hyperbolic conservation laws
 J. COMPUT. PHYS
, 1990
"... Many of the recently developed highresolution schemes for hyperbolic conservation laws are based on upwind differencing. The building block of these schemes is the averaging of an approximate Godunov solver; its time consuming part involves the fieldbyfield decomposition which is required in orde ..."
Abstract

Cited by 298 (25 self)
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Many of the recently developed highresolution schemes for hyperbolic conservation laws are based on upwind differencing. The building block of these schemes is the averaging of an approximate Godunov solver; its time consuming part involves the fieldbyfield decomposition which is required
Computing interface Motion in Compressible Gas Dynamics
, 1992
"... A “HamiltonJacobi” level set formulation of the equations of motion for propagating interfaces has been introduced recently by Osher and Sethian. This formulation allows fronts to selfintersect, develop singularities, and change topology. The numerical algorithms based on this approach handle topo ..."
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Cited by 102 (14 self)
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both conservative and nonconservative differencing of the level set function and compare the two approaches. To
Third Order Nonoscillatory Central Scheme For Hyperbolic Conservation Laws
"... . A thirdorder accurate Godunovtype scheme for the approximate solution of hyperbolic systems of conservation laws is presented. Its two main ingredients include: #1. A nonoscillatory piecewisequadratic reconstruction of pointvalues from their given cell averages; and #2. A central differencing ..."
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Cited by 69 (12 self)
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. A thirdorder accurate Godunovtype scheme for the approximate solution of hyperbolic systems of conservation laws is presented. Its two main ingredients include: #1. A nonoscillatory piecewisequadratic reconstruction of pointvalues from their given cell averages; and #2. A central differencing
Simplified Discretization of Systems of Hyperbolic Conservation Laws Containing Advection Equations
, 1999
"... The high speed flow of complex materials can often be modeled by the compressible Euler Equations coupled to (possibly many) additional advection equations. Traditionally, good computational results have been obtained by writing these systems in fully conservative form and applying the general metho ..."
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Cited by 16 (6 self)
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methodology of shockcapturing schemes for systems of hyperbolic conservation laws. In this paper, we show how to obtain the benefits of these schemes without the usual complexity of full characteristic decomposition or the restrictions imposed by fully conservative differencing. Instead, under certain
The penultimate scheme for systems of conservation laws: finitedifference ENO with Marquina’s flux splitting
, 1998
"... This paper provides a users’ guide to a new, general finite difference method for the numerical solution of systems of convection dominated conservation laws. We include both extensive motivation for the method design, as well as a detailed formulation suitable for direct implementation. Essentially ..."
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Cited by 27 (16 self)
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. Essentially NonOscillatory (ENO) methods are a class of high accuracy, shock capturing numerical methods for hyperbolic systems of conservation laws, based on upwind biased differencing in local characteristic fields. The earliest ENO methods used control volume discretizations, but subsequent work [12] has
EnergyConserving Simulation of Incompressible ElectroOsmotic and PressureDriven Flow
"... Abstract. A numerical model for electroosmotic flow is described. The advecting velocity field is computed by solving the incompressible Navier–Stokes equation. The method uses a semiimplicit multigrid algorithm to compute the divergencefree velocity at each grid point. The finite differences ar ..."
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Cited by 2 (2 self)
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are secondorder accurate and centered in space; however, the traditional secondorder compact finite differencing of the Poisson equation for the pressure field is shown not to conserve energy in the inviscid limit. We have designed a noncompact finite differencing for the Laplacian in the pressure
UNSTEADY IRROTATIONAL TRANSONIC FLOW ABOUT AIRFOILS
"... Numerical difference schemes are presented for the computation of unsteady transonic flows about airfoils. A firstorder system of equations in conservation form is developed for irrotational (full potential) flow and solved by finite difference methods. To enable the boundary conditions to be impos ..."
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to be imposed directly on the airfoil surface, a timevarying shearedrectilinear coordinate transformation is used. Explicit differencing schemes are used to solve both lifting and nonlifting cases. Additionally, an alternating direction implicit (ADI) scheme has been coded for efficient solutions in the non
c © Uma Publicação da Sociedade Brasileira de Matemática Aplicada e Computacional. Implementing Implicit Schemes in GENSMAC
"... Abstract. Implicit schemes are studied with the purpose of introducing them in the twodimensional GENSMAC method, for the numerical solution of unsteady newtonian incompressible flows. By using the fractionalstep approach, the Freeflow2D simulation system is employed to solve the conservation equ ..."
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equations. The viscous terms in the NavierStokes equations are implicitly treated via the Implicit Backward (IR), CrankNicolson (CN) and AdamsBashforth/CrankNicolson (AB/CN) schemes. The convective terms are explicitly treated by the upwind differencing Variable Order NonOscillatory Scheme (VONOS
Theoretical and Computational Fluid Dynamics EnergyConserving Simulation of Incompressible ElectroOsmotic and PressureDriven Flow
, 2002
"... Abstract. A numerical model for electroosmotic flow is described. The advecting velocity field is computed by solving the incompressible Navier–Stokes equation. The method uses a semiimplicit multigrid algorithm to compute the divergencefree velocity at each grid point. The finite differences ar ..."
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are secondorder accurate and centered in space; however, the traditional secondorder compact finite differencing of the Poisson equation for the pressure field is shown not to conserve energy in the inviscid limit. We have designed a noncompact finite differencing for the Laplacian in the pressure
Cosmological hydrodynamics with multispecies chemistry and nonequilibrium ionization and cooling
 New. A
, 1997
"... We have developed a method of solving for multispecies chemical reaction flows in non–equilibrium and self–consistently with the hydrodynamic equations in an expanding FLRW universe. The method is based on a backward differencing scheme for the required stability when solving stiff sets of equation ..."
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Cited by 9 (5 self)
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We have developed a method of solving for multispecies chemical reaction flows in non–equilibrium and self–consistently with the hydrodynamic equations in an expanding FLRW universe. The method is based on a backward differencing scheme for the required stability when solving stiff sets
Results 1  10
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