Answers for "how to make a select2 to add value out of options"

select2 clear options

Remove the selected options : 
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$('#mySelect2').val(null).trigger('change');

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Completly remove the select2 initialization :
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$('#payment_method').html('').select2({data: [{id: '', text: ''}]});

select2 add option

// Set the value, creating a new option if necessary
if ($('#mySelect2').find("option[value='" + data.id + "']").length) {
    $('#mySelect2').val(data.id).trigger('change');
} else { 
    // Create a DOM Option and pre-select by default
    var newOption = new Option(data.text, data.id, true, true);
    // Append it to the select
    $('#mySelect2').append(newOption).trigger('change');
}