Absorbing (non-reflecting) boundary condition

An absorbing BCs has been formulated and applied to SUIKOU2D in conjunction with MacCormack and TVD schemes. The inclusion of the boundaries is very important in the successful application of any numerical techniques. Hyperbolic equations are particularly sensitive because errors introduced at the boundaries are propagated and reflected throughout the grids. This, in many cases, may results in instability or incorrect flow values.

Numerical modeling of inundation flow often involves computational domains that are very large. Discretizing the entire domain and solving the flow equations turn out to be a tedious jobs in term of times and memory. Therefore, the physical domain has been truncated by introducing a pseudo boundary. Here, the use of pseudo boundary as open boundary aids in reducing the size of computational domain and and emphasizes the interest area only.

There are two possible flow conditions may occur in the pseudo boundary; sub-critical or super-critical flows accompanied with shocks where it needs special treatment on each. An ideal pseudo boundary condition should meet the following criteria:
(i) it should be compatible with physical conditions of the nature.
(ii) it should not degrade/defect the numerical solutions.
(iii) it should absorb the outgoing waves to avoid any reflections.

Several established methods are available for pseudo boundary. The simplest approach is by implementing two ways, including
1. extrapolation of flow variables from the interior node (Froude >=1);
2. solved by MoC (Froude <1).

Test Case

A 10m height of water in reservoir in upstream part of computational domain. It is assumed some buildings in the downstream part as represented by random blocks. Initially, it is dry in the downstream. Suddenly the reservoir partially bursts and inundates downstream part.

The simulations are carried out on the basis of;
a. The first case, all of outer BCs of the computational domain is considered as wall.
There is no incoming/outcoming flux through walls. The shocks will be reflected as they hit the walls.
b. Second, the downstream part is truncated by pseudo BC.
All incoming/outcoming shocks will be absorbed as represented flows pass through the downstream wall without any reflections.

The animations of water surface during 1200 seconds after breach are as shown below.
(click on the image to run animation)

a. case no.1 (walls BC).

b. case no 2. (non reflecting BC).


c. Water depth along x-axis at center of breach.

Obviously seen, the lowering water depth in reservoir occurs in case no. 2 since there is out flowing flux through pseudo BC, whilst no.1 is reflected back.

to be continued....