# 8.1.3. Boundary Conditions#

Boundary conditions are of crucial importance in CFD as they, in addition to the initial condition, ensure that the problem is well posed, which means that the solution of the system of partial differential equations (PDEs) is unique and consistent. The numerical boundary conditions must ensure that the interface between the domain interior and exterior resembles the physical phenomena, without adversely affecting the solution stability. The following section provides guidance for specifying boundary conditions in Flow360.

## 8.1.3.1. The Use of Expressions in Boundary Condition Inputs#

For a number of boundary conditions such as NoSlipWall, IsothermalWall and Freestream, a mathematical expression can be used to define the velocity field (Velocity). Expressions define a parameter based on component-wise independent variables [x,y,z]. The result will be evaluated and returned as the value of the parameter. The following operators are allowed to define an expression:

Symbol

Mathematical Operator

$$+$$

$$-$$

Subtraction

$$*$$

Multiplication

$$/$$

Division

$$\text{a^b}$$

Base a raised to the power b

$$sqrt()$$

Square-root

$$ln()$$

Natural Logarithm

$$exp()$$

Exponent

$$sin(), cos(), tan()$$

Trigonometric Functions

$$pi$$

Constant pi = 3.14158…