DispersiveLDGRHS1D.m

function [rhsu] = DispersiveLDGRHS1D(u,time)

% function [rhsu] = DispersiveLDGRHS1D(u,time)
% Purpose  : Evaluate RHS flux in 1D u_xxx using LDG fluxes and periodic BC's

Globals1D;

% Define field differences at faces, incl BC
du   = zeros(Nfp*Nfaces,K); du(:)     = u(vmapM)-u(vmapP);
uin  = u(vmapO);            du (mapI) = u(vmapI) - uin; 
uout = u(vmapI);            du (mapO) = u(vmapO) - uout;
fluxu = nx.*(1.0+nx).*du/2.0;

% Compute local variable p, define differences, incl BC
p = rx.*(Dr*u) - LIFT*(Fscale.*fluxu);
dp   = zeros(Nfp*Nfaces,K); dp(:)    = p(vmapM)-p(vmapP);
pin  = p(vmapO);            dp(mapI) = p(vmapI) - pin; 
pout = p(vmapI);            dp(mapO) = p(vmapO) - pout;
fluxp = nx.*(1.0-nx).*dp/2.0;

% Compute local variable q, define differences, incl BC
q = rx.*(Dr*p) - LIFT*(Fscale.*fluxp);
dq   = zeros(Nfp*Nfaces,K); dq(:)     = q(vmapM)-q(vmapP);
qin  = q(vmapO);            dq (mapI) = q(vmapI) - qin; 
qout = q(vmapI);            dq (mapO) = q(vmapO) - qout;
fluxq = nx.*(1.0-nx).*dq/2.0;

% compute right hand sides of the semi-discrete PDE
rhsu = rx.*(Dr*q) - LIFT*(Fscale.*fluxq);
return