Mean

Definition

In the case of spatial domain, it calculates mean of a given variable for a given container and returns it as shown in following equation. x_i is the i^th element’s variable value of the corresponding container. Result will have the same type as the type of the variable specified by the user. (If it has higher dimension than a scalar, mean of each dimension will be calculated seperately resulting with a mean having same dimension as the input dimension)

$$ \underline{r} = \frac{1}{N}\sum_{i=1}^{N}\underline{x}_i$$

In the case of temporal domain, Mean methods is the time integrated quantity’s mean for a specific variable. It will be stored each element under user specified variable and a user specified container. x_i is the i^th element’s variable value of the corresponding container. Result will have the same type as the type of the variable specified by the user preserving the dimensionality as in the spatial case.

$$\underline{\bar{x}} = \frac{1}{T_{total}}\sum_{k=1}^{P}{\underline{x}_k\Delta t_k} \quad where \quad T_{total} = T_{end} - T_{initial} \quad and \quad \Delta t_k = T_{k} - T_{k-1} \quad \forall T_k \in \left\lbrace T_{initial}, ..., T_{end} \right\rbrace $$

Examples

Spatial

Following is an example of mean calculation of non historical VELOCITY over the whole model part’s nodes

import KratosMultiphysics as Kratos
import KratosMultiphysics.StatisticsApplication as KratosStats
model = Kratos.Model()
model_part = model.CreateModelPart("test_model_part")
mean = KratosStats.SpatialMethods.NonHistorical.Nodes.ValueMethods.Mean(model_part, Kratos.VELOCITY)

Temporal

Following is an example of mean calculation of non historical velocity. Input variable is node’s non-historical container’s VELOCITY and output variable is same containers VECTOR_3D_MEAN where mean will be stored for each node. The 0 represents echo level for this method object. Blank “” indicates that value method is used.

import KratosMultiphysics as Kratos
import KratosMultiphysics.StatisticsApplication as KratosStats
model = Kratos.Model()
model_part = model.CreateModelPart("test_model_part")
mean_method = KratosStats.TemporalMethods.NonHistorical.Nodes.ValueMethods.Mean.Array(model_part, "", Kratos.VELOCITY, 0, KratosStats.VECTOR_3D_MEAN)
integration_starting_time = 2.0
mean_method.InitializeStatisticsMethod(integration_starting_time)
for t in range(3, 6):
    mean_method.CalculateStatistics()