clean up buoyancy routines -- some change to moist buoyancy (#1982)

* clean up buoyancy routines -- some change to moist buoyancy

* remove unused

* update amrex submodule and clean up buoyancy some more

* need to allow buoyancy_type 2 again

* remove shadowing

---------

Co-authored-by: Aaron M. Lattanzi <[email protected]>

Docs/sphinx_doc/LinearSolvers.rst

@@ -17,8 +17,9 @@ Multigrid can also be used when the union of grids at a level is not in itself r
 For simulations using grid stretching in the vertical but flat terrain, we must use the hybrid FFT solver in which
 we perform 2D transforms only in the lateral directions and couple the solution in the vertical direction with a tridiagonal solve.
 In both these cases we use a 7-point stencil.
+
 To solve the Poisson equation on terrain-fitted coordinates with general terrain,
 we rely on the FFT-preconditioned GMRES solver since the stencil effectively has variable coefficients and requires 19 points.
 
-   .. note::
-      **Currently only doubly periodic lateral boundary conditions are supported by the hybrid FFT, and therefore by the GMRES solver.  More general boundary conditions are a work in progress.**
+-   .. note::
+-      **The FFT solver / preconditioner can only be used when the union of grids at a level is itself rectangular.

Docs/sphinx_doc/theory/Buoyancy.rst

@@ -7,11 +7,24 @@
 
 .. _sec:Buoyancy:
 
+ERF has several options for how to define the buoyancy force.
+
 Buoyancy
 =========
 
-ERF has three options for how to define the buoyancy force.  Even in the absence of moisture these
-expressions are not equivalent.
+When using the anelastic formulation, the expression for buoyancy used by ERF is
+
+.. math::
+     \mathbf{B} = -\rho^\prime \mathbf{g} \approx -\rho_0 \mathbf{g} ( \frac{\theta_v^\prime}{\overline{\theta_0}}
+
+where we define
+
+.. math::
+     \theta_v = \theta_d (1 - (1 - \frac{R_v}{R_d}) (q_v + q_c) - \frac{R_v}{R_d} q_c)
+
+
+When using the compressible formulation, the following choices are available.
+
 
 Density of the mixture
 -----------------------
@@ -52,56 +65,10 @@ for the background state. For eg., a usual scenario is that of a background stat
 the total background density :math:`\rho_0 = \rho_{d_0}(1 + q_{v_0})`, where :math:`\rho_{d_0}` and :math:`q_{v_0}` are the background dry density and vapor mixing ratio respectively.
 As a check, we observe that :math:`\rho^\prime_0 = 0`, which means that the background state is not buoyant.
 
-Type 2
-------
-
-The second option for the buoyancy force is
-
-.. math::
-   \mathbf{B} = -\rho_0 \mathbf{g} ( 0.61 q_v^\prime - q_c^\prime - q_i^\prime - q_p^\prime
-                  + \frac{T^\prime}{\bar{T}} (1.0 + 0.61 \bar{q_v} - \bar{q_i} - \bar{q_c} - \bar{q_p}) )
-
-To derive this expression, we define :math:`T_v = T (1 + 0.61 q_v − q_c − q_i - q_p)`, then we can write
-
-.. math::
-    p = \rho (R_d q_d + R_v q_v) T = \rho R_d T (1 + 0.61 q_v − q_c − q_i - q_p ) = \rho R_d T_v
-
-
-Starting from :math:`p = \rho R_d T_v` and neglecting :math:`\frac{p^\prime}{\bar{p}}`, we now write
-
-.. math::
-   \frac{\rho^\prime}{\overline{\rho}} = -\frac{T_v^\prime}{\overline{T_v}}
-
-and define
-
-.. math::
-
-   T_v^\prime = T_v - \overline{T_v} \approx \overline{T} [ 0.61 q_v^\prime - (q_c^\prime + q_i^\prime + q_p^\prime)] +
-               (T - \overline{T}) [1+ 0.61 \bar{q_v} - \bar{q_c} - \bar{q_i} - \bar{q_p} ] .
-
-where we have retained only first order terms in perturbational quantities.
-
-Then
-
-.. math::
-
-   \mathbf{B} = \rho^\prime \mathbf{g} = -\overline{\rho} \frac{\overline{T}}{\overline{T_v}} \mathbf{g} [ 0.61 q_v^\prime - q_c^\prime - q_i^\prime - q_p^\prime ) + \frac{T^\prime}{\overline{T_v}} (1.0 + 0.61 \bar{q_v} - \bar{q_i} - \bar{q_c} - \bar{q_p}) ]
-
-where the overbar represents a horizontal average of the current state and the perturbation is defined relative to that average.
-
-Again keeping only the first order terms in the mass mixing ratios, we can simplify this to
-
-.. math::
-   \mathbf{B} = \rho^\prime \mathbf{g} = -\rho_0 \mathbf{g} [ 0.61 q_v^\prime - q_c^\prime + q_i^\prime + q_p^\prime
-                  + \frac{T^\prime}{\overline{T}} (1.0 + 0.61 \bar{q_v} - \bar{q_i} - \bar{q_c} - \bar{q_p}) ]
-
-We note that this reduces to Type 3 if the horizontal averages of the moisture terms are all zero.
-
 Type 3
 ------
 
-The third formulation of the buoyancy term assumes that the horizontal averages of the moisture quantities are negligible,
-which removes the need to compute horizontal averages of these quantities.   This reduces the Type 2 expression to the following:
+This formulation of the buoyancy term assumes that the horizontal averages of the moisture quantities are negligible.
 
 .. math::
      \mathbf{B} = \rho^\prime \mathbf{g} \approx -\rho_0 \mathbf{g} ( \frac{T^\prime}{\overline{T}}
@@ -120,7 +87,7 @@ This expression for buoyancy is from `khairoutdinov2003cloud`_ and `bryan2002ben
 .. math::
 
     \begin{equation}
-    \mathbf{B} = \rho'\mathbf{g} \approx -\rho\Bigg(\frac{T'}{T} + 0.61 q_v' - q_c - q_p - \frac{p'}{p}\Bigg)\mathbf{g},
+    \mathbf{B} = \rho'\mathbf{g} \approx -\rho \mathbf{g} \Bigg(\frac{T'}{T} + 0.61 q_v' - q_c - q_p - \frac{p'}{p}\Bigg)
     \end{equation}
 
 The derivation follows. The total density is given by :math:`\rho = \rho_d(1 + q_v + q_c + q_p)`, which can be written as

Source/DataStructs/ERF_DataStruct.H

@@ -126,14 +126,15 @@ struct SolverChoice {
             if (moisture_type == MoistureType::Kessler_NoRain ||
                 moisture_type == MoistureType::SAM ||
                 moisture_type == MoistureType::SAM_NoIce ||
-                moisture_type == MoistureType::SAM_NoPrecip_NoIce) {
-                buoyancy_type = 1; // asserted in make buoyancy
+                moisture_type == MoistureType::SAM_NoPrecip_NoIce)
+            {
+                buoyancy_type = 1; // uses Rhoprime
             } else {
                 buoyancy_type = 2; // uses Tprime
             }
         }
 
-        // Which expression (1,2 or 3) to use for buoyancy
+        // Which expression (1,2/3 or 4) to use for buoyancy
         pp.query("buoyancy_type", buoyancy_type);
 
         // What type of land surface model to use
@@ -196,7 +197,7 @@ struct SolverChoice {
         if (any_anelastic == 1) {
             constant_density = true;
             project_initial_velocity = true;
-            buoyancy_type = 2; // uses Tprime
+            buoyancy_type = 3; // (This isn't actually used when anelastic is set)
         } else {
             pp.query("project_initial_velocity", project_initial_velocity);