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!*****************************************************************************
!* A collection of one-dimensional Euler numerical fluxes, Version 4 (2010),
!*
!* written by Dr. Katate Masatsuka (info[at]cfdbooks.com),
!*
!* the author of useful CFD books, "I do like CFD" (http://www.cfdbooks.com).
!*
!*------------------------
!* List of Flux Functions:
!
! Lax-Friedrichs
! Richtmyer
! MacCormack
! Steger-Warming
! Van Leer
! AUSM
! Zha-Bilgen
! Godunov
! Osher
! Roe
! Rusanov
! HLL(HLLE)
! HLLL
! AUFS
!
!*------------------------
!*
!* These F90 routines were written and made available for download
!* for an educational purpose. Detailed description of each numerical
!* flux can be found in the original paper, or in popular textbooks, or
!* in the (will-be-available) second volume of "I do like CFD".
!*
!* Note that all routines are not efficiently implemented for clarity; you can
!* improve the efficiency and also you can covert it to double precision
!* version if you wish.
!*
!* Ver.5 (11-13-2013): Godunov flux corrected. (Thanks to Fran?ois Fraysse!)
!* Ver.4 (05-12-2010): AUFS flux added.
!* Ver.3 (05-11-2010): Godunov flux debugged.
!* Ver.2 (05-10-2010): Rusanov flux debugged.
!*
!* This file may be updated in future. (to add Hanel, HLLC, LDFSS, etc.)
!*****************************************************************************
!*****************************************************************************
!* --- Lax-Friedrichs's Flux Function ---
!*
!* P. D. Lax, Weak Solutions of Nonlinear Hyperbolic Equations and Their
!* Numerical Computation, Commun. Pure and Applied Mathematics, 7, 159-193,
!* 1954.
!*
!* This requires the function, physical_flux(u), included in this file.
!*
!* Katate Masatsuka, February 2009. http://www.cfdbooks.com
!*****************************************************************************
function LaxFriedrichs(uL,uR,dt,dx)
implicit none
real :: uL(3), uR(3), dt, dx ! Input (conservative variables rho*[1, v, E])
!* in the (will-be-available) second volume of "I do like CFD".
!*
!* Note that all routines are not efficiently implemented for clarity; you can
!* improve the efficiency and also you can covert it to double precision
!* version if you wish.
!*
!* Ver.5 (11-13-2013): Godunov flux corrected. (Thanks to Fran?ois Fraysse!)
!* Ver.4 (05-12-2010): AUFS flux added.
!* Ver.3 (05-11-2010): Godunov flux debugged.
!* Ver.2 (05-10-2010): Rusanov flux debugged.
!*
!* This file may be updated in future. (to add Hanel, HLLC, LDFSS, etc.)
!*****************************************************************************
!*****************************************************************************
!* --- Lax-Friedrichs's Flux Function ---
!*
!* P. D. Lax, Weak Solutions of Nonlinear Hyperbolic Equations and Their
!* Numerical Computation, Commun. Pure and Applied Mathematics, 7, 159-193,
!* 1954.
!*
!* This requires the function, physical_flux(u), included in this file.
!*
!* Katate Masatsuka, February 2009. http://www.cfdbooks.com
!*****************************************************************************
function LaxFriedrichs(uL,uR,dt,dx)
implicit none
real :: uL(3), uR(3), dt, dx ! Input (conservative variables rho*[1, v, E])
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