@@ -12,16 +12,16 @@ with $x\in[0,25]$ meters. Displacement and strain are derived from the pressure,
1212
1313#### Boundary conditions:
1414
15- - ** Dirichlet** at \( x = 0 \) : \( p(0,t) = 0 \)
16- - ** Neumann** at \( x = L \) : \( \frac{dp}{dx}(L,t) = 0 \)
15+ - ** Dirichlet** at $ x = 0$: $ p(0, t) = 0$
16+ - ** Neumann** at $ x = L$: $\displaystyle \frac{dp}{dx}(L, t) = 0$
1717
1818This corresponds to a domain with ** impermeable backing** and ** open drainage at the loaded end** .
1919
2020---
2121
2222#### Numerical Strategy
2323
24- - Pressure is initialized to a uniform value \( P_0 = 10 \text{ MPa} \)
24+ - Pressure is initialized to a uniform value $ P_0 = 10\ \mathrm{ MPa}$
2525- Integration is performed using ** Forward Euler**
2626- Mimetic MOLE operators:
2727 - ` lap() ` for pressure diffusion
@@ -62,17 +62,17 @@ At selected time snapshots (1, 10, 40, 70 hours), the following are printed and
6262
6363#### Physical Parameters
6464
65- | Parameter | Value | Description |
66- | ------------------| -------------------------------| --- --------------------------------------|
67- | \( P_0 \) | 10 MPa | Face load |
68- | \( c_f \) | \( 1 \times 10 ^{-4}\) | Diffusivity |
69- | \( K \) | \( 1 \times 10 ^{-12} \, \text {m}^2\) | Permeability |
70- | \( \mu \) | \( 1 \times 10 ^{-3} \, \text {Pa·s} \) | Dynamic viscosity |
71- | \( K_s \) | \( 1 \times 10^8 \, \text {Pa}\) | Bulk modulus |
72- | \( \ alpha \) | 1.0 | Biot coefficient |
73- | \( S_s \) | \( 1 \times 10 ^{-5} \, \text {Pa}^{-1}\) | Specific storage coefficient |
74- | \( \ rho \) | 1000 kg/m³ | Fluid density |
75- | \( g \) | 9.81 m/s² | Gravitational acceleration |
65+ | Parameter | Value | Description |
66+ | ----------: | ---------------------------------------| --------------------------------------|
67+ | $ P_0$ | 10 MPa | Face load |
68+ | $ c_f$ | $1\times10 ^{-4}$ | Diffusivity |
69+ | $K$ | $1\times10 ^{-12}\, \mathrm {m}^2$ | Permeability |
70+ | $\mu$ | $1\times10 ^{-3}\, \mathrm {Pa\cdot s}$ | Dynamic viscosity |
71+ | $ K_s$ | $1\times10^8 \, \mathrm {Pa}$ | Bulk modulus |
72+ | $\ alpha$ | 1.0 | Biot coefficient |
73+ | $ S_s$ | $1\times10 ^{-5}\, \mathrm {Pa}^{-1}$ | Specific storage coefficient |
74+ | $\ rho$ | $ 1000\, \mathrm{ kg/m^3}$ | Fluid density |
75+ | $g$ | $ 9.81\, \mathrm{ m/s^2}$ | Gravitational acceleration |
7676
7777---
7878
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