# laplacianFoam

Source: https://help.sim-flow.com/solvers/laplacian-foam
Last updated: 2026-10-14

## Description

laplacianFoam is a basic solver that simulates diffusion-driven scalar transport in both transient and steady-state forms. Primarily used for heat conduction, it efficiently incorporates volumetric heat sources in its computations.

While adept at managing homogeneous fluid properties and thermal diffusion equations, the solver does not extend to non-homogeneous fluid properties, turbulence, multiphase flows, or reactive flows. Its core application lies in modeling heat conduction in solids, guided by the Laplace and heat diffusion equations.

## Features

- **Steady-State and Transient**
- **Laplace Equation Solver for a Scalar Quantity**

- Heat Transfer

- Thermal Diffusion Model only
- Homogeneous Material Model
- Constant Diffusion Coefficient

## Application

**Heat Conduction**

- Heat Conduction in Solids
  e.g. flanges, bodies in contact with hot surfaces

## Heat Transfer Solvers

Heat Transfer Solvers In this group, we have included solvers that are designed to model: **Heat Transfer**, **Radiation**, **Natural** and **Forced Convection**, **Conjugate Heat Transfer (CHT)**.

**Heat Transfer, Single Fluid**

- [buoyantSimpleFoam](https://help.sim-flow.com/solvers/buoyant-simple-foam) steady-state, compressible, buoyancy-driven flow
- [buoyantPimpleFoam](https://help.sim-flow.com/solvers/buoyant-pimple-foam) transient, compressible, buoyancy-driven flow

**Heat Transfer, Single Fluid - Boussinesq**

- [buoyantBoussinesqSimpleFoam](https://help.sim-flow.com/solvers/buoyant-boussinesq-simple-foam) steady-state, incompressible, buoyancy using Boussinesq approximation
- [buoyantBoussinesqPimpleFoam](https://help.sim-flow.com/solvers/buoyant-boussinesq-pimple-foam) transient, incompressible, buoyancy using Boussinesq approximation

**Heat Transfer, Single Solid**

- [laplacianFoam](https://help.sim-flow.com/solvers/laplacian-foam) steady-state and transient, thermal conduction in solid
- [overLaplacianDyMFoam](https://help.sim-flow.com/solvers/over-laplacian-dym-foam) extension of laplacianFoam with Overset

**CHT, Multiple Fluids / Solids**

- [chtMultiRegionSimpleFoam](https://help.sim-flow.com/solvers/cht-multi-region-simple-foam) steady-state, compressible, arbitrary fluid and solid regions
- [chtMultiRegionFoam](https://help.sim-flow.com/solvers/cht-multi-region-foam) transient, compressible, arbitrary fluid and solid regions

- CHT - Conjugate Heat Transfer
- MRF - Multiple Reference Frame
- Overset - also known as Chimera Grid (Method)

## Results Fields

This solver provides the following results fields:

- **Primary Results Fields** - quantities produced by the solver as default outputs

**Primary Results Fields**

| Temperature | \(T\) [\(K\)] |
| --- | --- |

- ***Primary Results Fields** are metrics produced by the solver as default outputs.