update the scholarly contribution

Author: yzeng

Docs/IAMReX_documentation/source/DiffusedIBM.rst

@@ -142,5 +142,3 @@ In contrast to the prescribed kinematics case, the motion of a freely moving par
 On the right-hand side of :eq:`eq:particle1`-:eq:`eq:particle2`, the term :math:`\mathbf{F}_l^{n+1/2}` refers to the Lagrangian Force, coming from the final value of :math:`\mathbf{F}^{m}` in Algorithm-1_. The time derivatives of momentum integration :math:`\rho_f \frac{d}{d t}\left(\int_{V_p} \mathbf{u} d V\right)` and angular momentum integration :math:`\rho_f \frac{d}{d t}\left(\int_{V_p} \mathbf{r} \times \mathbf{u} d V\right)` within the particle are also included. These two integrated terms account for flow unsteadiness by using the PVF field (:ref:`R-PVF`). The term :math:`\left(\rho_p-\rho_f\right) V_p \mathbf{g}` considers the buoyancy effects. The terms :math:`\mathbf{F}_c^{n+1 / 2}` and :math:`\mathbf{T}_c^{n+1 / 2}` refer to the induced force and torque generated by the particle collision, respectively. If there is only one single particle in the system, both :math:`\mathbf{F}_c^{n+1 / 2}` and :math:`\mathbf{T}_c^{n+1 / 2}` are set to be zero. On the left-hand side of :eq:`eq:particle1`-:eq:`eq:particle2`, we use the second-order mid-point scheme to integrate particle motions . After updating the particle centroid velocity :math:`\mathbf{U}_{r}^{n+1}` and angular velocity :math:`\mathbf{W}_{r}^{n+1}` at :math:`t^{n+1}`, we go back to :eq:`eq:pr2` to update new position of the particle centroid :math:`\mathbf{X}_{r}^{n+1}`.
 
 The time advancement scheme in this work is not fully implicit , yet it can deal with the free motion applies to particles either with a large density ratio (i.e., :math:`\frac{\rho_p}{\rho_f} \geq 10`) or a small density ratio (i.e., :math:`\frac{\rho_p}{\rho_f} \approx 1.5 - 2`). We found it is robust and fast enough to handle all the testing cases in :ref:`Chap:Results`. Before ending this Section, we also emphasize that our method is similar to the "weak coupling" method used in the sharp-interfaced immersed boundary method, which requires only one solution for fluid and solid solver during each time step and no iterations are needed between these two solvers. It is easier to extend the current portable solver to the "strong coupling" method, which then re-projects the flow part, re-updates the solid particle, and performs a convergence checking between the fluid solver and the solid solver during each sub-iteration.
-
-More sophisticated treatments are possible

Docs/IAMReX_documentation/source/Software_Chapter.rst

@@ -6,13 +6,10 @@ IAMReX represents a significant enhancement to the baseline IAMR (Incompressible
 I. Two Enhanced Time Advancement Methods
 ----------------------------------------
 
-New Specialized Advance Functions
-^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
-
 IAMeX introduces two distinct time advancement methods, each targeting specific multi-physics scenarios:
 
 1. Two-Phase Flow with Level Set Method
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 - **Function**: ``NavierStokes::advance_semistaggered_twophase_ls()``
 - **Purpose**: Sharp interface tracking for immiscible two-phase flows
 - **Key Features**:
@@ -22,16 +19,16 @@ IAMeX introduces two distinct time advancement methods, each targeting specific
   - Heaviside function computation for material properties
 
 2. Fluid-Structure Interaction with Diffused Immersed Boundary Method (DIBM) and Particle Collision
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 - **Function**: ``NavierStokes::advance_semistaggered_fsi_diffusedib()``
 - **Purpose**: Robust fluid-solid coupling without mesh conformity
 - **Key Features**:
   - Particle-based immersed boundary implementation
   - 6-DOF rigid body dynamics
   - Collision detection and resolution
 
-II. Level Set Interface Tracking
---------------------------------
+II. Level Set Method
+--------------------
 
 Enhanced State Management
 ^^^^^^^^^^^^^^^^^^^^^^^^^
@@ -52,8 +49,8 @@ Key Computational Functions
 - ``NavierStokesBase::rk_second_reinit()``: Second RK step during reinitialization
 - ``NavierStokesBase::mass_fix()``: Mass fix subroutine during reinitialization
 
-Level Set Methodology
-^^^^^^^^^^^^^^^^^^^^^
+Features
+^^^^^^^^
 - **Sharp Interface**: Maintains interface thickness of 1.5~2 grid cells
 - **Mass Conservation**: Conservative advection schemes
 - **Reinitialization**: Periodic distance function correction
@@ -85,8 +82,8 @@ Particle Data Structure ( **kernel** )
         Vector<Real> phiK, thetaK;              // Spherical marker distribution
     }
 
-Key Computational Functions (**IBM**)
-^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+Key Computational functions
+^^^^^^^^^^^^^^^^^^^^^^^^^^^
 
 1. Fluid-Solid Coupling
 ~~~~~~~~~~~~~~~~~~~~~~~
@@ -118,8 +115,8 @@ Key Computational Functions (**IBM**)
 - **Collision Integration**: Seamless coupling with collision forces
 - ``nodal_phi_to_pvf()``: Particle volume fraction calculation
 
-Advanced Features
-^^^^^^^^^^^^^^^^^
+Features
+^^^^^^^^
 
 Marker Distribution
 ~~~~~~~~~~~~~~~~~~~