Tweak to fast integrator (erf-model#1435)

* minor tweak to fast substepping to be consistent with notes

* slight tweak to fast integrator to make it consistent with the notes

Source/TimeIntegration/ERF_fast_rhs_MT.cpp

@@ -56,7 +56,7 @@ void erf_fast_rhs_MT (int step, int nrk,
                       const Vector<MultiFab>& S_prev,                // if step == 0, this is S_old, else the previous solution
                       Vector<MultiFab>& S_stg_data,                  // at last RK stg: S^n, S^* or S^**
                       const MultiFab& S_stg_prim,                    // Primitive version of S_stg_data[IntVar::cons]
-                      const MultiFab& pi_stg,                        // Exner function evaluated at last RK stg
+                      const MultiFab& pi_stage,                      // Exner function evaluated at last RK stg
                       const MultiFab& fast_coeffs,                   // Coeffs for tridiagonal solve
                       Vector<MultiFab>& S_data,                      // S_sum = state at end of this substep
                       Vector<MultiFab>& S_scratch,                   // S_sum_old at most recent fast timestep for (rho theta)
@@ -173,7 +173,7 @@ void erf_fast_rhs_MT (int step, int nrk,
 
         const Array4<      Real>& omega_arr = Omega.array(mfi);
 
-        const Array4<const Real>& pi_stg_ca = pi_stg.const_array(mfi);
+        const Array4<const Real>& pi_stage_ca = pi_stage.const_array(mfi);
 
         const Array4<Real>& theta_extrap = extrap.array(mfi);
 
@@ -261,7 +261,7 @@ void erf_fast_rhs_MT (int step, int nrk,
                     gpx /= (1.0 + q);
                 }
 
-                Real pi_c =  0.5 * (pi_stg_ca(i-1,j,k,0) + pi_stg_ca(i  ,j,k,0));
+                Real pi_c =  0.5 * (pi_stage_ca(i-1,j,k,0) + pi_stage_ca(i  ,j,k,0));
                 Real fast_rhs_rho_u = -Gamma * R_d * pi_c * gpx;
 
                 // We have already scaled the source terms to have the extra factor of dJ
@@ -288,7 +288,7 @@ void erf_fast_rhs_MT (int step, int nrk,
                     gpy /= (1.0 + q);
                 }
 
-                Real pi_c =  0.5 * (pi_stg_ca(i,j-1,k,0) + pi_stg_ca(i,j  ,k,0));
+                Real pi_c =  0.5 * (pi_stage_ca(i,j-1,k,0) + pi_stage_ca(i,j  ,k,0));
                 Real fast_rhs_rho_v = -Gamma * R_d * pi_c * gpy;
 
                 // We have already scaled the source terms to have the extra factor of dJ

Source/TimeIntegration/ERF_fast_rhs_T.cpp

@@ -23,7 +23,7 @@ using namespace amrex;
  * @param[in]    S_prev previous solution
  * @param[in]    S_stage_data solution            at previous RK stage
  * @param[in]    S_stage_prim primitive variables at previous RK stage
- * @param[in]    pi_stage   Exner function      at previous RK stage
+ * @param[in]    pi_stage     Exner function      at previous RK stage
  * @param[in]    fast_coeffs coefficients for the tridiagonal solve used in the fast integrator
  * @param[out]   S_data current solution
  * @param[in]    S_scratch scratch space

Source/TimeIntegration/ERF_make_fast_coeffs.cpp

@@ -80,7 +80,8 @@ void make_fast_coeffs (int /*level*/,
         const Array4<const Real>& detJ   = l_use_terrain ?   detJ_cc->const_array(mfi) : Array4<const Real>{};
 
         const Array4<const Real>& r0_ca       = r0->const_array(mfi);
-        const Array4<const Real>& pi0_ca      = pi0->const_array(mfi); const Array4<const Real>& pi_stage_ca = pi_stage.const_array(mfi);
+        const Array4<const Real>& pi0_ca      = pi0->const_array(mfi);
+        const Array4<const Real>& pi_stage_ca = pi_stage.const_array(mfi);
 
         FArrayBox gam_fab; gam_fab.resize(surroundingNodes(bx,2),1,The_Async_Arena());
 
@@ -117,20 +118,20 @@ void make_fast_coeffs (int /*level*/,
                  pibar_lo = pi0_ca(i,j,k-1);
                  pibar_hi = pi0_ca(i,j,k  );
 
-                 Real pi_lo = pi_stage_ca(i,j,k-1,0);
-                 Real pi_hi = pi_stage_ca(i,j,k  ,0);
-                 Real pi_c =  0.5 * (pi_lo + pi_hi);
+                 Real pi_c =  0.5 * (pi_stage_ca(i,j,k-1,0) + pi_stage_ca(i,j,k,0));
 
                  Real     detJ_on_kface = 0.5 * (detJ(i,j,k) + detJ(i,j,k-1));
                  Real inv_detJ_on_kface = 1. / detJ_on_kface;
 
-                 Real coeff_P = -Gamma * R_d * pi_c * dzi * inv_detJ_on_kface
-                               +  halfg * R_d * rhobar_hi * pi_hi  /
+                 Real coeff_P = -Gamma * R_d * dzi * inv_detJ_on_kface
+                               +  halfg * R_d * rhobar_hi /
                                (  c_v * pibar_hi * stage_cons(i,j,k,RhoTheta_comp) );
+                 coeff_P *= pi_c;
 
-                 Real coeff_Q =  Gamma * R_d * pi_c * dzi * inv_detJ_on_kface
-                               + halfg * R_d * rhobar_lo * pi_lo  /
+                 Real coeff_Q =  Gamma * R_d * dzi * inv_detJ_on_kface
+                               + halfg * R_d * rhobar_lo /
                                ( c_v  * pibar_lo * stage_cons(i,j,k-1,RhoTheta_comp) );
+                 coeff_Q *= pi_c;
 
                  coeffP_a(i,j,k) = coeff_P;
                  coeffQ_a(i,j,k) = coeff_Q;
@@ -164,17 +165,17 @@ void make_fast_coeffs (int /*level*/,
                  pibar_lo = pi0_ca(i,j,k-1);
                  pibar_hi = pi0_ca(i,j,k  );
 
-                 Real pi_lo = pi_stage_ca(i,j,k-1,0);
-                 Real pi_hi = pi_stage_ca(i,j,k  ,0);
-                 Real pi_c =  0.5 * (pi_lo + pi_hi);
+                 Real pi_c =  0.5 * (pi_stage_ca(i,j,k-1,0) + pi_stage_ca(i,j,k,0));
 
-                 Real coeff_P = -Gamma * R_d * pi_c * dzi
-                              +  halfg * R_d * rhobar_hi * pi_hi  /
+                 Real coeff_P = -Gamma * R_d * dzi
+                              +  halfg * R_d * rhobar_hi /
                               (  c_v * pibar_hi * stage_cons(i,j,k,RhoTheta_comp) );
+                 coeff_P *= pi_c;
 
-                 Real coeff_Q = Gamma * R_d * pi_c * dzi
-                              + halfg * R_d * rhobar_lo * pi_lo  /
+                 Real coeff_Q = Gamma * R_d * dzi
+                              + halfg * R_d * rhobar_lo /
                               ( c_v  * pibar_lo * stage_cons(i,j,k-1,RhoTheta_comp) );
+                 coeff_Q *= pi_c;
 
                  coeffP_a(i,j,k) = coeff_P;
                  coeffQ_a(i,j,k) = coeff_Q;

Source/TimeIntegration/TI_headers.H

@@ -164,7 +164,7 @@ void erf_fast_rhs_MT (int step, int nrk, int level, int finest_level,
                       const amrex::Vector<amrex::MultiFab >& S_prev,
                       amrex::Vector<amrex::MultiFab >& S_stg_data,
                       const amrex::MultiFab& S_stg_prim,
-                      const amrex::MultiFab& pi_stg,
+                      const amrex::MultiFab& pi_stage,
                       const amrex::MultiFab& fast_coeffs,
                       amrex::Vector<amrex::MultiFab >& S_data,
                       amrex::Vector<amrex::MultiFab >& S_scratch,

Tests/ERFGoldFiles/DensityCurrent/Header

@@ -19,18 +19,12 @@ pressure
 100 25 100 
 0
 0
-0 4 10
+0 2 10
 10
--12800 -6400
+-12800 0
 0 100
 0 6400
--6400 0
-0 100
-0 6400
-0 6400
-0 100
-0 6400
-6400 12800
+0 12800
 0 100
 0 6400
 Level_0/Cell

Tests/ERFGoldFiles/DensityCurrent/Level_0/Cell_H

@@ -2,27 +2,19 @@
 1
 8
 0
-(4 0
-((0,0,0) (63,3,63) (0,0,0))
-((64,0,0) (127,3,63) (0,0,0))
-((128,0,0) (191,3,63) (0,0,0))
-((192,0,0) (255,3,63) (0,0,0))
+(2 0
+((0,0,0) (127,3,63) (0,0,0))
+((128,0,0) (255,3,63) (0,0,0))
 )
-4
+2
 FabOnDisk: Cell_D_00000 0
 FabOnDisk: Cell_D_00001 0
-FabOnDisk: Cell_D_00002 0
-FabOnDisk: Cell_D_00003 0
 
-4,8
-6.5098892847193790e-01,-2.0418835990748977e-03,0.0000000000000000e+00,-4.4803493663859122e-04,2.9999999984644018e+02,4.4463890028261158e+04,6.5098892858777935e-01,4.4463890017184007e+04,
-6.4836893180468114e-01,-7.9260529722221518e-01,0.0000000000000000e+00,-2.1904806103671612e+00,2.8340212496085053e+02,4.4463890028261158e+04,6.5098892858777935e-01,4.4213560173266931e+04,
-6.4836893180468114e-01,-9.5512978283271610e-01,0.0000000000000000e+00,-2.1904806103671257e+00,2.8340212496085059e+02,4.4463890028261158e+04,6.5098892858777935e-01,4.4213560173266931e+04,
-6.5098892847193790e-01,-1.5670219933390387e-03,0.0000000000000000e+00,-4.4803493663859122e-04,2.9999999984644018e+02,4.4463890028261158e+04,6.5098892858777935e-01,4.4463890017184007e+04,
+2,8
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-4,8
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-1.1567295136790348e+00,2.0418835990748977e-03,0.0000000000000000e+00,7.4403897400177922e-04,3.0000000000000006e+02,9.9432624223818915e+04,1.1567294111744995e+00,9.9432636559645209e+04,
+2,8
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+1.1615310052895496e+00,7.9260530344048652e-01,0.0000000000000000e+00,3.2286309960014881e-01,3.0002669784915167e+02,9.9432624223818915e+04,1.1567294111744995e+00,1.0001094754880578e+05,
 

Tests/ERFGoldFiles/DensityCurrent_detJ2/Header

@@ -19,18 +19,12 @@ pressure
 100 25 50 
 0
 0
-0 4 10
+0 2 10
 10
--12800 -6400
+-12800 0
 0 100
 0 3200
--6400 0
-0 100
-0 3200
-0 6400
-0 100
-0 3200
-6400 12800
+0 12800
 0 100
 0 3200
 Level_0/Cell

Tests/ERFGoldFiles/DensityCurrent_detJ2/Level_0/Cell_H

@@ -2,27 +2,19 @@
 1
 8
 0
-(4 0
-((0,0,0) (63,3,63) (0,0,0))
-((64,0,0) (127,3,63) (0,0,0))
-((128,0,0) (191,3,63) (0,0,0))
-((192,0,0) (255,3,63) (0,0,0))
+(2 0
+((0,0,0) (127,3,63) (0,0,0))
+((128,0,0) (255,3,63) (0,0,0))
 )
-4
+2
 FabOnDisk: Cell_D_00000 0
 FabOnDisk: Cell_D_00001 0
-FabOnDisk: Cell_D_00002 0
-FabOnDisk: Cell_D_00003 0
 
-4,8
-6.5098892847193790e-01,-2.0418835990748977e-03,0.0000000000000000e+00,-4.4803493663859111e-04,2.9999999984644018e+02,4.4463890028261158e+04,6.5098892858777935e-01,4.4463890017184007e+04,
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