Root Mean Square | Kratos Multiphysics Documentation

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Definition

In the case of spatial domain, it calculates root mean square 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, root mean square of each dimension will be calculated seperately resulting with a mean having same dimension as the input dimension)

$$\underline{r} = \sqrt{\frac{1}{N}\sum_{i=1}^{N}{\underline{x}^2_i} }$$

In the case of temporal domain, Root Mean Square methods is the time integrated quantity’s root mean square 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.

$$\underline{r} = \sqrt{\frac{1}{T_{total}}\sum_{k=1}^{P}{\underline{x}_k^2\Delta t_k}} \quad where \quad T_{total} = T_{end} - T_{initial} \quad and \quad \Delta t_k = T_{k} - T_{k-1} \quad \forall T_k \in \left\lbrace T_{initial}, ..., T_{end} \right\rbrace$$

Examples

Spatial

Following is an example of root mean square 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")
rms = KratosStats.SpatialMethods.NonHistorical.Nodes.ValueMethods.RootMeanSquare(model_part, Kratos.VELOCITY)

Temporal

Following is an example of root mean square 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 root mean square value 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")
rms_method = KratosStats.TemporalMethods.NonHistorical.Nodes.ValueMethods.RootMeanSquare.Array(model_part, "", Kratos.VELOCITY, 0, KratosStats.VECTOR_3D_MEAN)
integration_starting_time = 2.0
rms_method.InitializeStatisticsMethod(integration_starting_time)
for t in range(3, 6):
    rms_method.CalculateStatistics()