Table of contents

• Subsection 3.6.1 General Formulation
• Subsection 3.6.2 Time Integration
• Subsection 3.6.3 Discretization
• Subsection 3.6.4 Linearization of $\int_{B}\mathbf{F}\cdot\mathbf{S}^{s}\Grad\delta\mathbf{v}^{s}\,dV$
• Subsection 3.6.5 Linearization of $\int_{B}\boldsymbol{\tau}\cdot J\mathbf{F}^{-T}\Grad\delta\mathbf{w}\,dV$
• Subsection 3.6.6 Linearization of $\int_{B}\delta\mathbf{w}\cdot J\mathbf{F}^{-T}\cdot\Grad p\,dV$
• Subsection 3.6.7 Linearization of $\int_{B}\delta\mathbf{w}\cdot\rho^{f}\left[J\left(\dot{\mathbf{w}}+\dot{\mathbf{v}}^{s}\right)+\left(\Grad\mathbf{w}+\Grad\mathbf{v}^{s}\right)\cdot\mathbf{W}\right]\,dV$
• Subsection 3.6.8 Linearization of $\int_{B}\delta J^{f}\left[\frac{1}{J^{f}}\left(J\dot{J}^{f}+\Grad J^{f}\cdot\mathbf{W}\right)-\dot{J}\right]\,dV$
• Subsection 3.6.9 Linearization of $-\int_{B}\Grad\delta J^{f}\cdot\mathbf{W}\,dV$
• Subsection 3.6.10 Body force term $\int_{b}\delta\mathbf{w}\cdot\rho^{f}\mathbf{b}\,dv$
• Subsection 3.6.11 Fluid traction acting on solid interface
• Subsection 3.6.12 Special Boundary Conditions