Integrate the condensed-phase burn by operator splitting when rburn%substeps > 0

Added to the flow RHS, the burn ties the reaction time scale to the acoustic CFL: a fast burn forces a smaller step for the whole simulation. With rburn%substeps > 0 the flow is frozen and the ODE is integrated over the step in equal sub-steps, re-evaluating the mixture pressure from the frozen internal energy each one so the rate feels the coefficients moving as reactant becomes product. rburn%substeps = 0, the default, keeps the source in the RHS unchanged. Completing a sub-step hands over the reactant's remaining mass along with the last of its volume fraction; capping the two separately strands mass at zero volume, which the EOS then divides by. The rate law is now stated once and called by both integrators.

Author: sbryngelson

src/common/m_derived_types.fpp

@@ -526,11 +526,12 @@ module m_derived_types
     !> Condensed-phase reactive-burn (programmed pressure detonation) parameters. The rate is
     !> dlambda/dt = k (1 - lambda) ((p - pign)/pref)^n, optionally scaled by exp(-ta/T) when ta > 0.
     type reactive_burn_parameters
-        real(wp) :: k     !< Rate coefficient [1/s]
-        real(wp) :: pign  !< Ignition pressure threshold [Pa]
-        real(wp) :: pref  !< Reference pressure for the pressure drive [Pa]
-        real(wp) :: n     !< Pressure-drive exponent
-        real(wp) :: ta    !< Activation temperature [K] (0 = pure pressure-driven; > 0 adds exp(-ta/T))
+        real(wp) :: k         !< Rate coefficient [1/s]
+        real(wp) :: pign      !< Ignition pressure threshold [Pa]
+        real(wp) :: pref      !< Reference pressure for the pressure drive [Pa]
+        real(wp) :: n         !< Pressure-drive exponent
+        real(wp) :: ta        !< Activation temperature [K] (0 = pure pressure-driven; > 0 adds exp(-ta/T))
+        integer  :: substeps  !< Operator-split sub-steps per time step (0 = source added to the flow RHS)
     end type reactive_burn_parameters
 
     !> Lagrangian bubble parameters

src/common/m_global_parameters_common.fpp

@@ -339,6 +339,7 @@ contains
         rburn%pref = dflt_real
         rburn%n = dflt_real
         rburn%ta = 0._wp
+        rburn%substeps = 0
 
         ! Case-optimization params: under case-opt these are compile-time constants in sim (skip assignment); in pre/post
         ! MFC_CASE_OPTIMIZATION is always False so the block always executes there.

src/simulation/m_reactive_burn.fpp

@@ -15,14 +15,44 @@
 module m_reactive_burn
 
     use m_global_parameters
-    use m_variables_conversion, only: f_sg_thermal
+    use m_variables_conversion, only: f_sg_thermal, s_compute_mixture_coefficients, f_pressure
 
     implicit none
 
-    private; public :: s_compute_reactive_burn
+    private; public :: s_compute_reactive_burn, s_reactive_burn_substep
 
 contains
 
+    !> Programmed-burn rate dlambda/dt for one cell state. Both the RHS source and the operator-split integrator call this, so the
+    !! rate law is stated once.
+    !! @param pres             Mixture pressure
+    !! @param lambda           Reaction progress, i.e. the product volume fraction
+    !! @param alpha_rho_react  Reactant partial density, for the optional Arrhenius factor
+    !! @param alpha_react      Reactant volume fraction, for the optional Arrhenius factor
+    !! @param rate             dlambda/dt; zero below the ignition pressure and once the reactant is spent
+    subroutine s_burn_rate(pres, lambda, alpha_rho_react, alpha_react, rate)
+
+        $:GPU_ROUTINE(function_name='s_burn_rate', parallelism='[seq]', cray_inline=True)
+
+        real(wp), intent(in)  :: pres, lambda, alpha_rho_react, alpha_react
+        real(wp), intent(out) :: rate
+        real(wp)              :: drive
+
+        ! Pressure-driven programmed burn: fires only behind the shock (p > rburn%pign).
+        drive = (pres - rburn%pign)/rburn%pref
+        if (drive > 0._wp .and. lambda < 1._wp) then
+            rate = rburn%k*(1._wp - lambda)*drive**rburn%n
+            ! Optional Arrhenius dependence on the reactant phasic temperature from the stiffened-gas
+            ! EOS. rburn%ta = 0, the default, leaves the pure pressure-driven rate unchanged.
+            if (rburn%ta > 0._wp) then
+                rate = rate*exp(-rburn%ta/f_sg_thermal(pres, alpha_rho_react/alpha_react, isentrope_n(1), isentrope_B(1), cvs(1)))
+            end if
+        else
+            rate = 0._wp
+        end if
+
+    end subroutine s_burn_rate
+
     !> Add the programmed-burn reaction source to the continuity and volume-fraction RHS.
     !! @param rhs_vf     Right-hand-side accumulator (inout)
     !! @param q_cons_vf  Conserved variables (partial densities live here)
@@ -34,9 +64,9 @@ contains
         type(scalar_field), dimension(sys_size), intent(in)    :: q_cons_vf, q_prim_vf
         type(int_bounds_info), dimension(1:3), intent(in)      :: bounds
         integer                                                :: x, y, z
-        real(wp)                                               :: rho, pres, lambda, rate, mdot, drive, T_r
+        real(wp)                                               :: rho, pres, lambda, rate, mdot
 
-        $:GPU_PARALLEL_LOOP(collapse=3, private='[rho, pres, lambda, rate, mdot, drive, T_r]', copyin='[bounds]')
+        $:GPU_PARALLEL_LOOP(collapse=3, private='[rho, pres, lambda, rate, mdot]', copyin='[bounds]')
         do z = bounds(3)%beg, bounds(3)%end
             do y = bounds(2)%beg, bounds(2)%end
                 do x = bounds(1)%beg, bounds(1)%end
@@ -45,20 +75,9 @@ contains
                     pres = q_prim_vf(eqn_idx%E)%sf(x, y, z)
                     lambda = q_prim_vf(eqn_idx%adv%beg + 1)%sf(x, y, z)  ! reaction progress = product volume fraction
 
-                    ! pressure-driven programmed burn: fires only behind the shock (p > rburn%pign)
-                    drive = (pres - rburn%pign)/rburn%pref
-                    if (drive > 0._wp .and. lambda < 1._wp) then
-                        rate = rburn%k*(1._wp - lambda)*drive**rburn%n  ! dlambda/dt
-
-                        ! Optional Arrhenius temperature dependence: rate *= exp(-rburn%ta/T_r), with T_r the
-                        ! reactant phasic temperature from the stiffened-gas EOS T = (p + pi_inf)/((Gamma-1) rho cv).
-                        ! rburn%ta = 0 (default) leaves the pure pressure-driven rate unchanged.
-                        if (rburn%ta > 0._wp) then
-                            T_r = f_sg_thermal(pres, q_cons_vf(eqn_idx%cont%beg)%sf(x, y, z)/q_prim_vf(eqn_idx%adv%beg)%sf(x, y, &
-                                               & z), isentrope_n(1), isentrope_B(1), cvs(1))
-                            rate = rate*exp(-rburn%ta/T_r)
-                        end if
-
+                    call s_burn_rate(pres, lambda, q_cons_vf(eqn_idx%cont%beg)%sf(x, y, z), q_prim_vf(eqn_idx%adv%beg)%sf(x, y, &
+                                     & z), rate)
+                    if (rate > 0._wp) then
                         mdot = rho*rate  ! mass reactant -> product
 
                         ! continuity: reactant loses mass, product gains it
@@ -76,4 +95,84 @@ contains
 
     end subroutine s_compute_reactive_burn
 
+    !> Operator-split alternative to s_compute_reactive_burn, used when rburn%substeps > 0. The flow is frozen and the burn ODE is
+    !! integrated over one time step in equal sub-steps, so the reaction time scale is decoupled from the acoustic CFL. The mixture
+    !! pressure is re-evaluated from the frozen internal energy each sub-step, which is what carries the rate's own feedback: the
+    !! coefficients move as the reactant becomes product.
+    !! @param q_cons_vf  Conserved variables, updated in place
+    !! @param dtime      Time step to integrate across
+    !! @param bounds     Interior cell bounds
+    subroutine s_reactive_burn_substep(q_cons_vf, dtime, bounds)
+
+        type(scalar_field), dimension(sys_size), intent(inout) :: q_cons_vf
+        real(wp), intent(in)                                   :: dtime
+        type(int_bounds_info), dimension(1:3), intent(in)      :: bounds
+        integer                                                :: x, y, z, i, sub
+        real(wp)                                               :: rho, pres, lambda, rate
+        real(wp)                                               :: dt_sub, e_int, gamma_mix, pi_inf_mix, qv_mix
+        real(wp)                                               :: rho_mix, dlambda, dmass
+
+        #:if not MFC_CASE_OPTIMIZATION and USING_AMD
+            real(wp), dimension(3) :: alpha_rho, alpha
+        #:else
+            real(wp), dimension(num_fluids) :: alpha_rho, alpha
+        #:endif
+
+        dt_sub = dtime/real(rburn%substeps, wp)
+
+        $:GPU_PARALLEL_LOOP(collapse=3, private='[alpha_rho, alpha, rho, pres, lambda, rate, e_int, gamma_mix, pi_inf_mix, &
+                            & qv_mix, rho_mix, dlambda, dmass, i, sub]', copyin='[bounds, dt_sub]')
+        do z = bounds(3)%beg, bounds(3)%end
+            do y = bounds(2)%beg, bounds(2)%end
+                do x = bounds(1)%beg, bounds(1)%end
+                    $:GPU_LOOP(parallelism='[seq]')
+                    do i = 1, num_fluids
+                        alpha_rho(i) = q_cons_vf(i + eqn_idx%cont%beg - 1)%sf(x, y, z)
+                        alpha(i) = q_cons_vf(i + eqn_idx%adv%beg - 1)%sf(x, y, z)
+                    end do
+                    rho = alpha_rho(1) + alpha_rho(2)
+
+                    ! Internal energy per unit volume is what the burn conserves: it moves mass and volume
+                    ! between the phases, and the qv difference surfaces as pressure through the mixture EOS.
+                    e_int = q_cons_vf(eqn_idx%E)%sf(x, y, z)
+                    $:GPU_LOOP(parallelism='[seq]')
+                    do i = eqn_idx%mom%beg, eqn_idx%mom%end
+                        e_int = e_int - 0.5_wp*q_cons_vf(i)%sf(x, y, z)**2/rho
+                    end do
+
+                    $:GPU_LOOP(parallelism='[seq]')
+                    do sub = 1, rburn%substeps
+                        lambda = alpha(2)
+                        call s_compute_mixture_coefficients(alpha_rho, alpha, rho_mix, gamma_mix, pi_inf_mix, qv_mix)
+                        pres = f_pressure(e_int, gamma_mix, pi_inf_mix, qv_mix)
+                        call s_burn_rate(pres, lambda, alpha_rho(1), alpha(1), rate)
+                        if (rate <= 0._wp) exit
+                        ! A sub-step longer than the reaction time would carry the progress variable past one.
+                        ! Stop it there and hand over the reactant's remaining mass in the same sub-step: capping
+                        ! the two independently strands mass at zero volume, and the EOS divides one by the other.
+                        if (rate*dt_sub >= 1._wp - lambda) then
+                            dlambda = 1._wp - lambda
+                            dmass = alpha_rho(1)
+                        else
+                            dlambda = rate*dt_sub
+                            dmass = min(rho*dlambda, alpha_rho(1))
+                        end if
+                        alpha(1) = alpha(1) - dlambda
+                        alpha(2) = alpha(2) + dlambda
+                        alpha_rho(1) = alpha_rho(1) - dmass
+                        alpha_rho(2) = alpha_rho(2) + dmass
+                    end do
+
+                    $:GPU_LOOP(parallelism='[seq]')
+                    do i = 1, num_fluids
+                        q_cons_vf(i + eqn_idx%cont%beg - 1)%sf(x, y, z) = alpha_rho(i)
+                        q_cons_vf(i + eqn_idx%adv%beg - 1)%sf(x, y, z) = alpha(i)
+                    end do
+                end do
+            end do
+        end do
+        $:END_GPU_PARALLEL_LOOP()
+
+    end subroutine s_reactive_burn_substep
+
 end module m_reactive_burn

src/simulation/m_rhs.fpp

@@ -869,7 +869,9 @@ contains
             call nvtxEndRange
         end if
 
-        if (reactive_burn) then
+        ! With rburn%substeps > 0 the burn is integrated by operator splitting after the flow
+        ! update (s_reactive_burn_substep), not added to the flow RHS here.
+        if (reactive_burn .and. rburn%substeps == 0) then
             call nvtxStartRange("RHS-REACTIVE-BURN")
             call s_compute_reactive_burn(rhs_vf, q_cons_qp%vf, q_prim_qp%vf, idwint)
             call nvtxEndRange

src/simulation/m_time_steppers.fpp

@@ -12,6 +12,7 @@ module m_time_steppers
     use m_global_parameters
     use m_rhs
     use m_chemistry
+    use m_reactive_burn, only: s_reactive_burn_substep
     use m_pressure_relaxation
     use m_data_output
     use m_bubbles_EE
@@ -585,6 +586,14 @@ contains
             call nvtxEndRange
         end if
 
+        ! Operator-split condensed-phase burn: integrate the progress variable per cell after the flow
+        ! update, with sub-stepping, instead of adding the source to the flow RHS (rburn%substeps > 0).
+        if (reactive_burn .and. rburn%substeps > 0) then
+            call nvtxStartRange("BURN-SUBSTEP")
+            call s_reactive_burn_substep(q_cons_ts(1)%vf, dt, idwint)
+            call nvtxEndRange
+        end if
+
         if (ib) then
             if (moving_immersed_boundary_flag) then
                 call s_wrap_periodic_ibs()  ! wraps the positions of IBs to the local proc