!--------------------------------------------------------------------------
   !---------------------------- compute_NH_geopot ----------------------------------
   tau2_g=tau*tau/g
   g2=g*g
   gm2 = 1./g2
   vreff = Treff*cpp/preff*kappa
   gamma = 1./(1.-kappa)
   !$OMP BARRIER
   ! compute Phi_star
   !$OMP DO SCHEDULE(STATIC)
   DO ij=1,primal_num
      DO l = 1,llm+1
         Phi_star_il(l,ij) = Phi_il(l,ij) + tau*g2*(W_il(l,ij)/m_il(l,ij)-tau)
      END DO
   END DO
   !$OMP END DO
   ! Newton-Raphson iteration : Phi_il contains current guess value
   DO iter=1,2 ! 2 iterations should be enough
      ! Compute pressure, A_ik
      SELECT CASE(caldyn_thermo)
      CASE(thermo_theta)
         !$OMP DO SCHEDULE(STATIC)
         DO ij=1,primal_num
            DO l = 1,llm
               rho_ij = (g*m_ik(l,ij))/(Phi_il(l+1,ij)-Phi_il(l,ij))
               X_ij = (cpp/preff)*kappa*theta(l,ij)*rho_ij
               p_ik(l,ij) = preff*(X_ij**gamma)
               c2_mik = gamma*p_ik(l,ij)/(rho_ij*m_ik(l,ij)) ! c^2 = gamma*R*T = gamma*p/rho
               A_ik(l,ij) = c2_mik*(tau/g*rho_ij)**2
            END DO
         END DO
         !$OMP END DO
      CASE(thermo_entropy)
         !$OMP DO SCHEDULE(STATIC)
         DO ij=1,primal_num
            DO l = 1,llm
               rho_ij = (g*m_ik(l,ij))/(Phi_il(l+1,ij)-Phi_il(l,ij))
               X_ij = log(vreff*rho_ij) + theta(l,ij)/cpp
               p_ik(l,ij) = preff*exp(X_ij*gamma)
               c2_mik = gamma*p_ik(l,ij)/(rho_ij*m_ik(l,ij)) ! c^2 = gamma*R*T = gamma*p/rho
               A_ik(l,ij) = c2_mik*(tau/g*rho_ij)**2
            END DO
         END DO
         !$OMP END DO
      CASE DEFAULT
         PRINT *, 'caldyn_thermo not supported by compute_NH_geopot', caldyn_thermo
         STOP
      END SELECT
      ! NB : A(1), A(llm), R(1), R(llm+1) = 0 => x(l)=0 at l=1,llm+1 => flat, rigid top and bottom
      ! Solve -A(l-1)x(l-1) + B(l)x(l) - A(l)x(l+1) = R(l) using Thomas algorithm
      !$OMP DO SCHEDULE(STATIC)
      DO ij=1,primal_num
         ! Compute residual R_il and B_il
         ! bottom interface l=1
         ml_g2 = gm2*m_il(1,ij)
         B_il(1,ij) = A_ik(1,ij) + ml_g2 + tau2_g*rho_bot
         R_il(1,ij) = ml_g2*( Phi_il(1,ij)-Phi_star_il(1,ij)) &
         + tau2_g*( p_ik(1,ij)-pbot+rho_bot*(Phi_il(1,ij)-PHI_BOT(ij)) )
         DO l = 2,llm
            ! inner interfaces
            ml_g2 = gm2*m_il(l,ij)
            B_il(l,ij) = A_ik(l,ij)+A_ik(l-1,ij) + ml_g2
            R_il(l,ij) = ml_g2*( Phi_il(l,ij)-Phi_star_il(l,ij)) &
            + tau2_g*(p_ik(l,ij)-p_ik(l-1,ij))
            ! consistency check : if Wil=0 and initial state is in hydrostatic balance
            ! then Phi_star_il(l,ij) = Phi_il(l,ij) - tau^2*g^2
            ! and residual = tau^2*(ml+(1/g)dl_pi)=0
         END DO
         ! top interface l=llm+1
         ml_g2 = gm2*m_il(llm+1,ij)
         B_il(llm+1,ij) = A_ik(llm+1 -1,ij) + ml_g2
         R_il(llm+1,ij) = ml_g2*( Phi_il(llm+1,ij)-Phi_star_il(llm+1,ij)) &
         + tau2_g*( ptop-p_ik(llm+1 -1,ij) )
         !
         ! Forward sweep :
         ! C(0)=0, C(l) = -A(l) / (B(l)+A(l-1)C(l-1)),
         ! D(0)=0, D(l) = (R(l)+A(l-1)D(l-1)) / (B(l)+A(l-1)C(l-1))
         X_ij = 1./B_il(1,ij)
         C_ik(1,ij) = -A_ik(1,ij) * X_ij
         D_il(1,ij) = R_il(1,ij) * X_ij
         DO l = 2,llm
            X_ij = 1./( B_il(l,ij) + A_ik(l-1,ij)*C_ik(l-1,ij) )
            C_ik(l,ij) = -A_ik(l,ij) * X_ij
            D_il(l,ij) = (R_il(l,ij)+A_ik(l-1,ij)*D_il(l-1,ij)) * X_ij
         END DO
         X_ij = 1./( B_il(llm+1,ij) + A_ik(llm+1 -1,ij)*C_ik(llm+1 -1,ij) )
         D_il(llm+1,ij) = (R_il(llm+1,ij)+A_ik(llm+1 -1,ij)*D_il(llm+1 -1,ij)) * X_ij
         ! Back substitution :
         ! x(i) = D(i)-C(i)x(i+1), x(llm+1)=0
         ! + Newton-Raphson update
         ! top interface l=llm+1
         x_il(llm+1,ij) = D_il(llm+1,ij)
         Phi_il(llm+1,ij) = Phi_il(llm+1,ij) - x_il(llm+1,ij)
         DO l = llm,1,-1
            ! Back substitution at lower interfaces
            x_il(l,ij) = D_il(l,ij) - C_ik(l,ij)*x_il(l+1,ij)
            Phi_il(l,ij) = Phi_il(l,ij) - x_il(l,ij)
         END DO
      END DO
      !$OMP END DO
      IF(debug_hevi_solver) THEN
         PRINT *, '[hevi_solver] A,B', iter, MAXVAL(ABS(A_ik)),MAXVAL(ABS(B_il))
         PRINT *, '[hevi_solver] C,D', iter, MAXVAL(ABS(C_ik)),MAXVAL(ABS(D_il))
         DO l=1,llm+1
            WRITE(*,'(A,I2.1,I3.2,E9.2)') '[hevi_solver] x_il', iter,l, MAXVAL(ABS(x_il(l,:)))
         END DO
         DO l=1,llm+1
            WRITE(*,'(A,I2.1,I3.2,E9.2)') '[hevi_solver] R_il', iter,l, MAXVAL(ABS(R_il(l,:)))
         END DO
      END IF
   END DO ! Newton-Raphson
   !$OMP BARRIER
   debug_hevi_solver=.FALSE.
   !---------------------------- compute_NH_geopot ----------------------------------
   !--------------------------------------------------------------------------