CFD Simulation for Battery Thermal Management

This repository contains a Computational Fluid Dynamics (CFD) simulation for battery thermal management using finite difference methods. The code solves coupled Navier-Stokes equations for fluid flow and energy equations for heat transfer, including battery heat generation effects.

Features

• 2D incompressible flow simulation
• Staggered grid formulation (MAC scheme)
• Upwind advection and central diffusion schemes
• Pressure-velocity coupling (Projection Method)
• Heat transfer with conduction/advection
• Battery heat generation modeling
• Obstacle handling with masked arrays
• Animated visualization of results

Numerical Methods

Equation Type	Discretized Form	Numerical Scheme
X-Momentum	∂u/∂t + u∂u/∂x + v∂u/∂y = ν(∂²u/∂x² + ∂²u/∂y²) - (1/ρ)∂p/∂x	Upwind (advection), Central (diffusion)
Y-Momentum	∂v/∂t + u∂v/∂x + v∂v/∂y = ν(∂²v/∂x² + ∂²v/∂y²) - (1/ρ)∂p/∂y	Upwind (advection), Central (diffusion)
Pressure Poisson	∇²p = ρ/Δt(∇·u*)	Jacobi Iteration
Energy Equation	ρc_p(∂T/∂t + u∂T/∂x + v∂T/∂y) = k(∂²T/∂x² + ∂²T/∂y²) + q_gen	Upwind (advection), Central (conduction)

Grid Discretization

Grid Type	Staggering	Dimensions	Note
Pressure (P)	Cell-centered	(ny+2) x (nx+2)	Extended boundary cells
U-Velocity	Staggered in x-direction	(ny+2) x (nx+1)	Located at cell faces
V-Velocity	Staggered in y-direction	(ny+1) x (nx+2)	Located at cell faces
Temperature	Cell-centered	(ny+2) x (nx+2)	Same as pressure grid

Boundary Conditions

Boundary Type	Velocity Treatment	Temperature Treatment	Pressure Treatment
Inlet	Dirichlet (fixed velocity)	Dirichlet (fixed temp)	Neumann (∂p/∂n = 0)
Outlet	Neumann (zero gradient)	Neumann (zero gradient)	Dirichlet (p = 0)
Walls	No-slip (u=v=0)	Adiabatic (∂T/∂n = 0)	Neumann (∂p/∂n = 0)
Obstacles	No-slip (u=v=0)	Heat generation source	Solid cells masked

Key Parameters

Parameter	Value	Description
Domain Size (Lx x Ly)	0.1 m x 0.1 m	Simulation domain dimensions
Grid Resolution	100 x 100	nx x ny cells
Time Step (Δt)	0.0001 s	CFL-condition compliant
Fluid Density	970 kg/m³	Coolant density
Battery Heat Gen	0 W/m³	Heat generation rate (configurable)

Results Visualization

The code generates three animations:

1. battery_temperature.mp4 - Temperature field evolution
2. velocity_field.mp4 - Velocity magnitude contours
3. pressure_field.mp4 - Pressure distribution