To filter dimension value through code in ax 2012

qbdsProjTable = _query.dataSourceTable(tableNum(ProjTable));
           
        SysQuery::addDimensionAttributeRange(_query, qbdsProjTable.name(), fieldStr(ProjTable, DefaultDimension), DimensionComponent::DimensionAttribute, "Diving", "LineofBusiness", true);

Find Dimension Name based on default dimemsion

The following method can be created in DimensionDefaultingEngine class and used wherever required.

public static SysDim  umg_DefaultDimensionValue(DimensionDefault   _dimensionDefault, Description  _segmentName)
{
    DimensionAttributeValueSetStorage       dimensionStorage;
    Counter                                 i;
    SysDim                                  segmentValue;

    // Get dimension storage
    if (_dimensionDefault)
    {
        dimensionStorage = DimensionAttributeValueSetStorage::find(_dimensionDefault);
        for (i=1 ; i<= dimensionStorage.elements() ; i++)
        {
            if (DimensionAttribute::find(dimensionStorage.getAttributeByIndex(i)).Name == _segmentName)
            {
                segmentValue = dimensionStorage.getDisplayValueByIndex(i);
                break;
            }
            else
            {
                segmentValue = '';
            }
        }
    }
    return segmentValue;
}