5.4. Spectral filters

mirgecom.filter is for filters and filter-related constructs.

Discussion of the spectral filter design can be found in: [Hesthaven_2008], Section 5.3

5.4.1. Mode Response Functions

mirgecom.filter.exponential_mode_response_function(mode, alpha, cutoff, nfilt, filter_order)

Return an exponential filter coefficient for the user-provided mode.

5.4.2. Helper Functions

mirgecom.filter.make_spectral_filter(actx, group, cutoff, mode_response_function)

Create a spectral filter with the provided mode_response_function.

This routine returns a filter operator in the modal basis designed to apply the user-provided mode_response_function to the spectral modes beyond the user-provided cutoff.

Parameters:

• actx (arraycontext.ArrayContext) – A arraycontext.ArrayContext associated with an array of degrees of freedom

• group (meshmode.mesh.MeshElementGroup) – A meshmode.mesh.MeshElementGroup from which the mode ids, element order, and dimension may be retrieved.

• cutoff (int) – Mode cutoff beyond which the filter will be applied, and below which the filter will preserve.

• mode_response_function – A function that returns a filter weight for for each mode id.

Returns:

filter – filter operator in the modal basis

Return type:

numpy.ndarray

mirgecom.filter.apply_spectral_filter(actx, modal_field, discr, cutoff, mode_response_function)

Apply the spectral filter, defined by the mode_response_function.

This routine returns filtered data in the modal basis, which has been applied using a user-provided mode_response_function to dampen modes beyond the user-provided cutoff.

Parameters:

• actx (arraycontext.ArrayContext) – A arraycontext.ArrayContext associated with an array of degrees of freedom

• modal_field (numpy.ndarray) – DOFArray or object array of DOFArrays denoting the modal data

• discr (meshmode.discretization.Discretization) – A meshmode.discretization.Discretization describing the volume discretization the modal_field comes from.

• cutoff (int) – Mode cutoff beyond which the filter will be applied, and below which the filter will preserve.

• mode_response_function – A function that returns a filter weight for for each mode id.

Returns:

modal_field – DOFArray or object array of DOFArrays

Return type:

meshmode.dof_array.DOFArray

5.4.3. Applying Filters

mirgecom.filter.filter_modally(dcoll, cutoff, mode_resp_func, field, *, dd=DOFDesc(domain_tag=VolumeDomainTag(tag=<class 'grudge.dof_desc.VTAG_ALL'>), discretization_tag=<class 'grudge.dof_desc.DISCR_TAG_BASE'>))

Stand-alone procedural interface to spectral filtering.

For each element group in the discretization, and restriction, This routine generates:

• a filter operator:

  • cutoff filters only modes above this mode id

  • mode_resp_func function returns a filter coefficient

    for a given mode

  • memoized into the array context

• a filtered solution wherein the filter is applied to field.

Parameters:

• dcoll (grudge.discretization.DiscretizationCollection) – Grudge discretization with boundaries object

• cutoff (int) – Mode below which field will not be filtered

• mode_resp_func – Modal response function returns a filter coefficient for input mode id

• field (mirgecom.fluid.ConservedVars) – An array container containing the relevant field(s) to filter.

• dd (grudge.dof_desc.DOFDesc) – Describe the type of DOF vector on which to operate. Must be on the base discretization.

Returns:

result – An array container containing the filtered field(s).

Return type:

mirgecom.fluid.ConservedVars

5.4.4. Spectral Analysis Helpers

mirgecom.filter.get_element_spectrum_from_modal_representation(actx, vol_discr, modal_fields, element_order)

Get the Legendre Polynomial expansion for specified fields on elements.

Parameters:

• actx (arraycontext.ArrayContext) – A arraycontext.ArrayContext associated with an array of degrees of freedom

• vol_discr (grudge.discretization.DiscretizationCollection) – Grudge discretization for volume elements only

• modal_fields (numpy.ndarray) – Array of DOFArrays with modal respresentations for each field

• element_order (int) – Polynomial order for the elements in the discretization

Returns:

Array with the element modes accumulated into the corresponding “modes” for the polynomial basis functions for each field.

Return type:

numpy.ndarray